Details

analyze3.0s (16.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5015	432
0	6	6
1	6	6

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

Symmetry

(sort M D)

Compiler

Compiled 19 to 19 computations (0% saved)

sample86.0ms (0.5%)

Algorithm

1×

intervals

Results

32.0ms	256×	body	128	valid
9.0ms	92×	body	128	nan
3.0ms	37×	body	128	invalid

Compiler

Compiled 37 to 43 computations (-16.2% saved)

simplify65.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

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

Error

12.6b

Counts

2 → 1

Compiler

Compiled 36 to 36 computations (0% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
9.4b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite304.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

6.5b

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

Counts

4 → 116

Calls

4 calls:

16.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
12.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
6.0ms	(/.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))))

Compiler

Compiled 3444 to 1962 computations (43% saved)

series2.0s (11%)

Error

6.6b

Counts

4 → 61

Calls

4 calls:

671.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
671.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
387.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
167.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3842 to 3404 computations (11.4% saved)

simplify104.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5054	3992

prune279.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	166	11	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	167	11	178

Error

3.9b

Counts

178 → 11

Compiler

Compiled 4302 to 2298 computations (46.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
9.1b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))

rewrite209.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

69×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
26×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
21×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
19×	`add-sqr-sqrt_binary64_1123`
13×	`add-cube-cbrt_binary64_1136` `-un-lft-identity_binary64_1101` `times-frac_binary64_1107` `associate-r*_binary64_1041`
7×	`pow1_binary64_1162`
5×	`associate-l_binary64_1042`
4×	`add-log-exp_binary64_1140` `div-inv_binary64_1098`
3×	`sqrt-prod_binary64_1117`
2×	`unswap-sqr_binary64_1069` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l_binary64_1046` `associate-/r_binary64_1045` `sqrt-div_binary64_1118`
1×	`pow-prod-down_binary64_1172` `frac-times_binary64_1111` `associate-l/_binary64_1044` `associate-r/_binary64_1043` `*-commutative_binary64_1032` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `rem-sqrt-square_binary64_1114`

Counts

4 → 109

Calls

4 calls:

12.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3773 to 1881 computations (50.1% saved)

series1.1s (6.1%)

Error

3.3b

Counts

4 → 50

Calls

4 calls:

396.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
330.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
170.0ms	(/.f64 (.f64 M D) (.f64 2 d))
145.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3467 to 2688 computations (22.5% saved)

simplify94.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5005	2799

prune224.0ms (1.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	155	4	159
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	159	11	170

Error

2.5b

Counts

170 → 11

Compiler

Compiled 4470 to 2175 computations (51.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 h (.f64 1/2 (/.f64 (.f64 M D) d))) l))))
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
5.4b	(/.f64 (*.f64 M D) d)
7.7b	(/.f64 (.f64 h (.f64 1/2 (/.f64 (*.f64 M D) d))) l)

rewrite186.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

2.5b

Rules

41×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
13×	`prod-exp_binary64_1150` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cbrt-unprod_binary64_1134`
10×	`add-sqr-sqrt_binary64_1123`
9×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
7×	`times-frac_binary64_1107` `associate-/r*_binary64_1045`
5×	`pow1_binary64_1162`
4×	`add-log-exp_binary64_1140`
3×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/l*_binary64_1046` `sqrt-prod_binary64_1117`
2×	`associate-*r/_binary64_1043` `sqrt-div_binary64_1118`
1×	`associate-/l/_binary64_1048` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `flip3--_binary64_1105` `flip--_binary64_1076` `rem-sqrt-square_binary64_1114`

Counts

4 → 85

Calls

4 calls:

11.0ms	(/.f64 (.f64 h (.f64 1/2 (/.f64 (*.f64 M D) d))) l)
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 h (.f64 1/2 (/.f64 (.f64 M D) d))) l))))
5.0ms	(/.f64 (*.f64 M D) d)

Compiler

Compiled 2875 to 1456 computations (49.4% saved)

series1.1s (5.9%)

Error

2.5b

Counts

4 → 50

Calls

4 calls:

443.0ms	(/.f64 (.f64 h (.f64 1/2 (/.f64 (*.f64 M D) d))) l)
332.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 h (.f64 1/2 (/.f64 (.f64 M D) d))) l))))
120.0ms	(/.f64 (.f64 M D) (.f64 2 d))
113.0ms	(/.f64 (*.f64 M D) d)

Compiler

Compiled 3467 to 2678 computations (22.8% saved)

simplify69.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4989	2325
1	4989	2325

prune202.0ms (1.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	135	11	146

Error

2.5b

Counts

146 → 11

Compiler

Compiled 3799 to 1889 computations (50.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.0b	(/.f64 (.f64 1/2 (/.f64 (.f64 M D) d)) l)
5.4b	(/.f64 (.f64 M D) (.f64 2 d))
5.4b	(/.f64 (*.f64 M D) d)
5.7b	(.f64 h (/.f64 (.f64 1/2 (/.f64 (*.f64 M D) d)) l))

rewrite189.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

2.5b

Rules

55×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
18×	`prod-exp_binary64_1150` `div-exp_binary64_1152` `cbrt-unprod_binary64_1134` `cbrt-undiv_binary64_1135`
13×	`add-sqr-sqrt_binary64_1123`
11×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
10×	`times-frac_binary64_1107`
7×	`associate-r_binary64_1041` `associate-/r*_binary64_1045`
6×	`pow1_binary64_1162`
4×	`add-log-exp_binary64_1140` `div-inv_binary64_1098`
3×	`associate-l_binary64_1042` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l*_binary64_1046`
2×	`associate-*r/_binary64_1043`
1×	`pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `*-commutative_binary64_1032` `associate-/l/_binary64_1048`

Counts

4 → 99

Calls

4 calls:

11.0ms	(.f64 h (/.f64 (.f64 1/2 (/.f64 (*.f64 M D) d)) l))
7.0ms	(/.f64 (.f64 1/2 (/.f64 (.f64 M D) d)) l)
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(/.f64 (*.f64 M D) d)

Compiler

Compiled 3134 to 1543 computations (50.8% saved)

series1.0s (5.6%)

Error

2.5b

Counts

4 → 45

Calls

4 calls:

439.0ms	(.f64 h (/.f64 (.f64 1/2 (/.f64 (*.f64 M D) d)) l))
240.0ms	(/.f64 (.f64 1/2 (/.f64 (.f64 M D) d)) l)
142.0ms	(/.f64 (*.f64 M D) d)
140.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3240 to 2314 computations (28.6% saved)

simplify119.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4985	1924
1	4985	1924

prune169.0ms (0.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	144	11	155

Error

2.5b

Counts

155 → 11

Compiler

Compiled 3837 to 1858 computations (51.6% saved)

regimes3.3s (18.1%)

Accuracy

Total 5.2b remaining (60.9%)

Threshold costs 0b (0%)

Compiler

Compiled 34000 to 28843 computations (15.2% saved)

bsearch7.0ms (0%)

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

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	128	72
1	128	72

Compiler

Compiled 96 to 70 computations (27.1% saved)

end0.0ms (0%)

sample4.1s (23.1%)

Algorithm

1×

intervals

Results

729.0ms	8000×	body	128	valid
269.0ms	3109×	body	128	nan
120.0ms	1326×	body	128	invalid

Compiler

Compiled 1945 to 1640 computations (15.7% saved)

Details

analyze3.0s (16.9%)

sample86.0ms (0.5%)

simplify65.0ms (0.4%)

prune3.0ms (0%)

localize17.0ms (0.1%)

rewrite304.0ms (1.7%)

series2.0s (11%)

simplify104.0ms (0.6%)

prune279.0ms (1.6%)

localize16.0ms (0.1%)

rewrite209.0ms (1.2%)

series1.1s (6.1%)

simplify94.0ms (0.5%)

prune224.0ms (1.2%)

localize16.0ms (0.1%)

rewrite186.0ms (1%)

series1.1s (5.9%)

simplify69.0ms (0.4%)

prune202.0ms (1.1%)

localize17.0ms (0.1%)

rewrite189.0ms (1.1%)

series1.0s (5.6%)

simplify119.0ms (0.7%)

prune169.0ms (0.9%)

regimes3.3s (18.1%)

bsearch7.0ms (0%)

simplify15.0ms (0.1%)

end0.0ms (0%)

sample4.1s (23.1%)

Profiling