Details

analyze2.2s (16.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 19 to 19 computations (0% saved)

sample45.0ms (0.3%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
7.0ms	88×	body	128	nan
2.0ms	32×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify206.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	6100	27

prune3.0ms (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

Merged error: 16.4b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
5.1b	(/.f64 (.f64 M D) (.f64 2 d))
5.6b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
10.7b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite49.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_1139`
38×	`add-sqr-sqrt_binary64_1123`
27×	`prod-exp_binary64_1150`
23×	`add-cbrt-cube_binary64_1137`
19×	`associate-r_binary64_1041` `div-exp_binary64_1152`
17×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
15×	`times-frac_binary64_1107`
13×	`associate-l_binary64_1042`
10×	`pow-exp_binary64_1169` `unswap-sqr_binary64_1069`
7×	`cbrt-unprod_binary64_1134` `unpow-prod-down_binary64_1180` `pow1_binary64_1162` `sqrt-prod_binary64_1117`
5×	`cbrt-undiv_binary64_1135`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
3×	`associate-*r/_binary64_1043` `div-inv_binary64_1098` `sqr-pow_binary64_1073` `unpow2_binary64_1166`
2×	`*-commutative_binary64_1032` `flip--_binary64_1076` `flip3--_binary64_1105` `pow-to-exp_binary64_1170`
1×	`rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `associate-/l_binary64_1046` `pow-prod-down_binary64_1172` `associate-/r_binary64_1045` `pow1/2_binary64_1181`

Counts

4 → 116

Calls

4 calls:

13.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
12.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

series1.1s (7.8%)

Counts

4 → 12

Calls

4 calls:

521.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
322.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
167.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
42.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify55.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5599	2845

prune197.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	118	10	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	10	129

Merged error: 9.4b

Counts

129 → 10

Compiler

Compiled 3420 to 2006 computations (41.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.8b	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
5.1b	(/.f64 (.f64 M D) (.f64 2 d))
5.6b	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
5.8b	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))

rewrite52.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`add-exp-log_binary64_1139`
91×	`prod-exp_binary64_1150`
40×	`div-exp_binary64_1152`
30×	`add-cbrt-cube_binary64_1137`
25×	`pow-exp_binary64_1169`
23×	`associate-r_binary64_1041`
22×	`add-sqr-sqrt_binary64_1123`
15×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
11×	`cbrt-unprod_binary64_1134` `times-frac_binary64_1107`
8×	`1-exp_binary64_1145` `rec-exp_binary64_1151`
7×	`pow1_binary64_1162`
6×	`unpow-prod-down_binary64_1180` `cbrt-undiv_binary64_1135`
5×	`pow-to-exp_binary64_1170`
4×	`add-log-exp_binary64_1140` `associate-l_binary64_1042` `unswap-sqr_binary64_1069`
3×	`sqrt-prod_binary64_1117` `div-inv_binary64_1098`
2×	`*-commutative_binary64_1032` `sqrt-div_binary64_1118` `sqr-pow_binary64_1073` `unpow2_binary64_1166`
1×	`rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-r/_binary64_1043` `associate-/l_binary64_1046` `pow-prod-down_binary64_1172` `associate-/r*_binary64_1045` `pow1/2_binary64_1181` `un-div-inv_binary64_1099`

Counts

4 → 130

Calls

4 calls:

13.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
9.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
9.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series1.0s (7.6%)

Counts

4 → 12

Calls

4 calls:

601.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))))
200.0ms	(.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) (/.f64 1 l))
172.0ms	(.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2))
43.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify58.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5297	2765

prune205.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	137	5	142
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	141	11	152

Merged error: 8.7b

Counts

152 → 11

Compiler

Compiled 3649 to 2427 computations (33.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.1b	(/.f64 (.f64 M D) (.f64 2 d))
5.1b	(/.f64 (.f64 M D) (.f64 2 d))
5.6b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 1 l))))
5.8b	(.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 1 l))

rewrite111.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

879×	`add-exp-log_binary64_1139`
528×	`prod-exp_binary64_1150`
469×	`add-cbrt-cube_binary64_1137`
268×	`cbrt-unprod_binary64_1134`
246×	`div-exp_binary64_1152`
127×	`cbrt-undiv_binary64_1135`
31×	`1-exp_binary64_1145` `rec-exp_binary64_1151`
14×	`pow1_binary64_1162`
13×	`add-sqr-sqrt_binary64_1123` `associate-r_binary64_1041`
12×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
11×	`times-frac_binary64_1107`
7×	`associate-*r/_binary64_1043`
6×	`pow-prod-down_binary64_1172`
5×	`frac-times_binary64_1111` `associate-*l/_binary64_1044`
4×	`add-log-exp_binary64_1140`
3×	`sqrt-prod_binary64_1117` `div-inv_binary64_1098`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `sqrt-div_binary64_1118` `associate-/r_binary64_1045`
1×	`-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-l*_binary64_1042` `pow1/2_binary64_1181` `un-div-inv_binary64_1099`

Counts

4 → 276

Calls

4 calls:

27.0ms	(.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 1 l))
9.0ms	(/.f64 (.f64 M D) (.f64 2 d))
9.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 1 l))))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))

series878.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

584.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 1 l))))
209.0ms	(.f64 (.f64 (.f64 h (/.f64 (.f64 M D) (.f64 2 d))) (/.f64 (.f64 M D) (*.f64 2 d))) (/.f64 1 l))
44.0ms	(/.f64 (.f64 M D) (.f64 2 d))
40.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify146.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4950	6701
1	4950	6701

prune386.0ms (2.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	286	2	288
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	289	10	299

Merged error: 8.5b

Counts

299 → 10

Compiler

Compiled 7370 to 4421 computations (40% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.6b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))))) (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) 2)) (/.f64 1 l))))
5.8b	(.f64 (.f64 (.f64 h (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))))) (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) 2)) (/.f64 1 l))
18.3b	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
18.3b	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))

rewrite85.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

486×	`add-exp-log_binary64_1139`
352×	`prod-exp_binary64_1150`
92×	`div-exp_binary64_1152`
86×	`add-cbrt-cube_binary64_1137`
60×	`cbrt-unprod_binary64_1134`
28×	`pow-exp_binary64_1169` `pow-to-exp_binary64_1170`
22×	`1-exp_binary64_1145` `rec-exp_binary64_1151`
16×	`cbrt-undiv_binary64_1135`
15×	`add-sqr-sqrt_binary64_1123`
14×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
13×	`associate-r_binary64_1041`
11×	`times-frac_binary64_1107` `associate-*l/_binary64_1044`
10×	`cbrt-prod_binary64_1132`
9×	`associate-*r/_binary64_1043`
7×	`pow1_binary64_1162`
6×	`cbrt-div_binary64_1133`
5×	`frac-times_binary64_1111`
4×	`add-log-exp_binary64_1140`
3×	`sqrt-prod_binary64_1117` `div-inv_binary64_1098`
2×	`pow1/3_binary64_1183` `sqrt-div_binary64_1118`
1×	`-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `flip--_binary64_1076` `flip3--_binary64_1105` `pow-prod-down_binary64_1172` `associate-l*_binary64_1042` `pow1/2_binary64_1181` `un-div-inv_binary64_1099`

Counts

4 → 178

Calls

4 calls:

28.0ms	(.f64 (.f64 (.f64 h (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))))) (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) 2)) (/.f64 1 l))
11.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))))) (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) 2)) (/.f64 1 l))))
5.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
5.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))

series1.7s (12.5%)

Counts

4 → 12

Calls

4 calls:

921.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 h (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))))) (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) 2)) (/.f64 1 l))))
406.0ms	(.f64 (.f64 (.f64 h (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))))) (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) 2)) (/.f64 1 l))
178.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))
168.0ms	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))

simplify125.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4951	4362
1	4951	4362

prune278.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	190	10	200

Merged error: 8.5b

Counts

200 → 10

Compiler

Compiled 5223 to 3357 computations (35.7% saved)

regimes1.9s (14.4%)

Compiler: Compiled 22196 to 19016 computations (14.3% saved)

bsearch3.0ms (0%)

Compiler: Compiled 3 to 7 computations (-133.3% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	282	148
1	282	148

end0.0ms (0%)

sample2.6s (19.3%)

Algorithm

1×

intervals

Results

618.0ms	8000×	body	128	valid
252.0ms	3199×	body	128	nan
103.0ms	1272×	body	128	invalid

Compiler

Compiled 1488 to 1250 computations (16% saved)

Details

analyze2.2s (16.4%)

sample45.0ms (0.3%)

simplify206.0ms (1.5%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite49.0ms (0.4%)

series1.1s (7.8%)

simplify55.0ms (0.4%)

prune197.0ms (1.5%)

localize15.0ms (0.1%)

rewrite52.0ms (0.4%)

series1.0s (7.6%)

simplify58.0ms (0.4%)

prune205.0ms (1.5%)

localize14.0ms (0.1%)

rewrite111.0ms (0.8%)

series878.0ms (6.5%)

simplify146.0ms (1.1%)

prune386.0ms (2.9%)

localize19.0ms (0.1%)

rewrite85.0ms (0.6%)

series1.7s (12.5%)

simplify125.0ms (0.9%)

prune278.0ms (2.1%)

regimes1.9s (14.4%)

bsearch3.0ms (0%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample2.6s (19.3%)

Profiling