Details

analyze668.0ms (2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6300	74
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

Symmetry

(sort alpha beta)

Compiler

Compiled 42 to 29 computations (31% saved)

sample76.0ms (0.2%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
8.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify441.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (429.0ms)

Iter	Nodes	Cost
0	5023	37

prune10.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

1.0b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.0b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
14.3b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite740.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

77×	`*-un-lft-identity_binary64_1101`
34×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `distribute-lft-out_binary64_1052`
24×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
21×	`add-sqr-sqrt_binary64_1123` `associate-r_binary64_1041`
18×	`associate-/r/_binary64_1047`
16×	`frac-times_binary64_1111`
15×	`add-cube-cbrt_binary64_1136`
14×	`times-frac_binary64_1107`
13×	`pow1_binary64_1162`
11×	`swap-sqr_binary64_1068`
10×	`prod-exp_binary64_1150` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cbrt-unprod_binary64_1134` `associate-*l/_binary64_1044`
9×	`associate-l_binary64_1042`
8×	`associate-*r/_binary64_1043`
7×	`associate-/l/_binary64_1048`
6×	`associate-/r*_binary64_1045`
5×	`associate-/l*_binary64_1046`
4×	`add-log-exp_binary64_1140`
3×	`div-inv_binary64_1098` `unswap-sqr_binary64_1069`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `pow-prod-down_binary64_1172` `*-commutative_binary64_1032`
1×	`pow2_binary64_1182` `pow-prod-up_binary64_1171` `pow-plus_binary64_1164` `pow-sqr_binary64_1074` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050`

Counts

4 → 158

Calls

4 calls:

49.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
44.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
31.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
30.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

Compiler

Compiled 6017 to 3676 computations (38.9% saved)

series2.9s (8.4%)

Error

0.0b

Counts

4 → 66

Calls

4 calls:

1.2s	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
616.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
427.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
230.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

Compiler

Compiled 10229 to 8094 computations (20.9% saved)

simplify169.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5177	9969

prune909.0ms (2.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	218	6	224
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	220	6	226

Error

0.0b

Counts

226 → 6

Compiler

Compiled 9682 to 6464 computations (33.2% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
0.1b	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))
0.1b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))
0.3b	(.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))

rewrite1.4s (4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

223×	`*-un-lft-identity_binary64_1101`
110×	`times-frac_binary64_1107`
92×	`distribute-lft-out_binary64_1052`
68×	`sqrt-prod_binary64_1117`
64×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123`
58×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
41×	`associate-r_binary64_1041`
20×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
19×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
18×	`frac-times_binary64_1111` `associate-*l/_binary64_1044`
15×	`associate-/l/_binary64_1048` `associate-/l_binary64_1046` `associate-/r_binary64_1045`
14×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
9×	`pow1_binary64_1162`
8×	`associate-/r/_binary64_1047`
6×	`associate-*r/_binary64_1043`
4×	`add-log-exp_binary64_1140` `div-inv_binary64_1098` `sqrt-div_binary64_1118`
3×	`pow-prod-down_binary64_1172` `frac-2neg_binary64_1112` `clear-num_binary64_1100`
1×	`associate-l_binary64_1042` `*-commutative_binary64_1032`

Counts

4 → 249

Calls

4 calls:

63.0ms	(.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
61.0ms	(/.f64 (.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
20.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))
18.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 11031 to 7735 computations (29.9% saved)

series3.0s (8.8%)

Error

0.0b

Counts

4 → 55

Calls

4 calls:

1.3s	(/.f64 (.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
910.0ms	(.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
201.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))
199.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 10302 to 8146 computations (20.9% saved)

simplify241.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5471	12599

prune1.6s (4.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	303	1	304
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	305	5	310

Error

Counts

310 → 5

Compiler

Compiled 13624 to 9601 computations (29.5% saved)

localize42.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 (*.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
0.1b	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))
0.1b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))
0.3b	(.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))

rewrite1.9s (5.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

235×	`*-un-lft-identity_binary64_1101`
152×	`add-exp-log_binary64_1139`
120×	`times-frac_binary64_1107`
95×	`distribute-lft-out_binary64_1052`
94×	`add-cbrt-cube_binary64_1137`
78×	`prod-exp_binary64_1150`
71×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123`
68×	`sqrt-prod_binary64_1117`
62×	`associate-r_binary64_1041`
44×	`cbrt-unprod_binary64_1134`
41×	`div-exp_binary64_1152`
38×	`frac-times_binary64_1111` `associate-*l/_binary64_1044`
24×	`cbrt-undiv_binary64_1135`
18×	`pow1_binary64_1162` `flip3-+_binary64_1104` `flip-+_binary64_1075`
14×	`associate-/l*_binary64_1046`
10×	`associate-r/_binary64_1043` `associate-/r_binary64_1045`
9×	`pow-prod-down_binary64_1172`
8×	`associate-/r/_binary64_1047`
7×	`1-exp_binary64_1145` `rec-exp_binary64_1151`
4×	`add-log-exp_binary64_1140` `div-inv_binary64_1098` `sqrt-div_binary64_1118` `associate-/l/_binary64_1048`
2×	`associate-l_binary64_1042` `*-commutative_binary64_1032` `frac-2neg_binary64_1112` `clear-num_binary64_1100`
1×	`un-div-inv_binary64_1099`

Counts

4 → 300

Calls

4 calls:

78.0ms	(.f64 (.f64 (*.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
65.0ms	(.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
20.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))
19.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 14062 to 10076 computations (28.3% saved)

series3.2s (9.3%)

Error

Counts

4 → 55

Calls

4 calls:

1.4s	(.f64 (.f64 (*.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
978.0ms	(.f64 (.f64 (+.f64 1 alpha) (/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
219.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))
211.0ms	(/.f64 (sqrt.f64 (+.f64 1 beta)) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 10484 to 8328 computations (20.6% saved)

simplify295.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

355 → 355

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5547	14781

prune1.9s (5.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	355	0	355
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	355	5	360

Error

Counts

360 → 5

Compiler

Compiled 15641 to 11178 computations (28.5% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (.f64 (+.f64 alpha 1) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (.f64 (+.f64 alpha (+.f64 2 beta)) (+.f64 alpha (+.f64 2 beta)))) 3))) (+.f64 alpha (+.f64 beta 3)))
0.1b	(pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 alpha (+.f64 2 beta)) (+.f64 alpha (+.f64 2 beta)))) 3)
14.3b	(/.f64 (+.f64 1 beta) (*.f64 (+.f64 alpha (+.f64 2 beta)) (+.f64 alpha (+.f64 2 beta))))
20.3b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 alpha (+.f64 2 beta)) (+.f64 alpha (+.f64 2 beta)))) 3))

rewrite881.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

42×	`associate-/r/_binary64_1047`
40×	`*-un-lft-identity_binary64_1101`
38×	`cbrt-prod_binary64_1132`
34×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
32×	`unpow-prod-down_binary64_1180` `cube-prod_binary64_1129`
25×	`times-frac_binary64_1107`
22×	`frac-times_binary64_1111`
20×	`add-exp-log_binary64_1139`
19×	`add-cbrt-cube_binary64_1137`
18×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123`
12×	`distribute-lft-out_binary64_1052` `associate-*l/_binary64_1044`
11×	`associate-*r/_binary64_1043`
7×	`associate-/l/_binary64_1048`
6×	`div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `associate-/r*_binary64_1045`
5×	`pow1_binary64_1162` `cube-div_binary64_1130` `associate-/l*_binary64_1046`
4×	`add-log-exp_binary64_1140` `cbrt-div_binary64_1133`
3×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `pow-unpow_binary64_1178` `pow-exp_binary64_1169` `rem-cube-cbrt_binary64_1124`
2×	`unpow3_binary64_1167` `cube-mult_binary64_1131` `sqr-pow_binary64_1073` `frac-2neg_binary64_1112` `clear-num_binary64_1100`
1×	`pow1/3_binary64_1183` `rem-cbrt-cube_binary64_1125` `pow-pow_binary64_1173` `pow-to-exp_binary64_1170`

Counts

4 → 167

Calls

4 calls:

41.0ms	(/.f64 (.f64 (+.f64 alpha 1) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (.f64 (+.f64 alpha (+.f64 2 beta)) (+.f64 alpha (+.f64 2 beta)))) 3))) (+.f64 alpha (+.f64 beta 3)))
36.0ms	(pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 alpha (+.f64 2 beta)) (+.f64 alpha (+.f64 2 beta)))) 3)
32.0ms	(/.f64 (+.f64 1 beta) (*.f64 (+.f64 alpha (+.f64 2 beta)) (+.f64 alpha (+.f64 2 beta))))
18.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 alpha (+.f64 2 beta)) (+.f64 alpha (+.f64 2 beta)))) 3))

Compiler

Compiled 7370 to 5303 computations (28% saved)

series3.9s (11.5%)

Error

Counts

4 → 64

Calls

4 calls:

1.4s	(pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 alpha (+.f64 2 beta)) (+.f64 alpha (+.f64 2 beta)))) 3)
1.2s	(/.f64 (.f64 (+.f64 alpha 1) (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (.f64 (+.f64 alpha (+.f64 2 beta)) (+.f64 alpha (+.f64 2 beta)))) 3))) (+.f64 alpha (+.f64 beta 3)))
452.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 1 beta) (*.f64 (+.f64 alpha (+.f64 2 beta)) (+.f64 alpha (+.f64 2 beta)))) 3))
440.0ms	(/.f64 (+.f64 1 beta) (*.f64 (+.f64 alpha (+.f64 2 beta)) (+.f64 alpha (+.f64 2 beta))))

Compiler

Compiled 11738 to 9442 computations (19.6% saved)

simplify221.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4973	11360
1	4973	11360

prune1.2s (3.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	231	5	236

Error

Counts

236 → 5

Compiler

Compiled 10549 to 7600 computations (28% saved)

regimes1.3s (3.9%)

Accuracy

Total 0.1b remaining (92.2%)

Threshold costs 0.1b (92.2%)

Compiler

Compiled 11195 to 8486 computations (24.2% saved)

bsearch0.0ms (0%)

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	37
1	24	37

Remove

(sort alpha beta)

Compiler

Compiled 50 to 36 computations (28% saved)

end0.0ms (0%)

sample7.0s (20.6%)

Algorithm

1×

intervals

Results

960.0ms	8000×	body	128	valid
241.0ms	8000×	pre	128	true

Compiler

Compiled 3774 to 2859 computations (24.2% saved)

Details

analyze668.0ms (2%)

sample76.0ms (0.2%)

simplify441.0ms (1.3%)

prune10.0ms (0%)

localize31.0ms (0.1%)

rewrite740.0ms (2.2%)

series2.9s (8.4%)

simplify169.0ms (0.5%)

prune909.0ms (2.7%)

localize34.0ms (0.1%)

rewrite1.4s (4%)

series3.0s (8.8%)

simplify241.0ms (0.7%)

prune1.6s (4.8%)

localize42.0ms (0.1%)

rewrite1.9s (5.6%)

series3.2s (9.3%)

simplify295.0ms (0.9%)

prune1.9s (5.6%)

localize31.0ms (0.1%)

rewrite881.0ms (2.6%)

series3.9s (11.5%)

simplify221.0ms (0.6%)

prune1.2s (3.5%)

regimes1.3s (3.9%)

bsearch0.0ms (0%)

simplify17.0ms (0.1%)

end0.0ms (0%)

sample7.0s (20.6%)

Profiling