Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample71.0ms (1.4%)

Algorithm

1×

intervals

Results

44.0ms	128×	body	1024	valid
12.0ms	62×	body	512	valid
5.0ms	9×	body	2048	valid
3.0ms	31×	body	256	valid
1.0ms	26×	body	128	valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify366.0ms (7.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (200.0ms)

Iter	Nodes	Cost
0	4989	12
1	4989	12

prune2.0ms (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: 57.8b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
6.1b	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64_1088`
52×	`add-sqr-sqrt_binary64_1109`
48×	`times-frac_binary64_1094`
30×	`log-prod_binary64_1171`
25×	`add-cube-cbrt_binary64_1120`
18×	`difference-of-squares_binary64_1057`
13×	`distribute-lft-out_binary64_1041`
9×	`distribute-lft-out--_binary64_1042`
7×	`add-exp-log_binary64_1123`
6×	`associate-/l*_binary64_1035`
4×	`add-cbrt-cube_binary64_1121` `associate-/r*_binary64_1034` `associate-/r/_binary64_1036`
3×	`pow1_binary64_1146`
2×	`rem-log-exp_binary64_1126` `associate-/l/_binary64_1037` `div-exp_binary64_1136` `flip-+_binary64_1062` `add-log-exp_binary64_1124` `flip3-+_binary64_1091` `div-inv_binary64_1085`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `log-pow_binary64_1174` `flip3--_binary64_1092` `flip--_binary64_1063` `div-sub_binary64_1093` `log-div_binary64_1172` `cbrt-undiv_binary64_1119`

Counts

2 → 92

Calls

2 calls:

10.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
9.0ms	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

series85.0ms (1.7%)

Counts

2 → 6

Calls

2 calls:

57.0ms	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
27.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))

simplify73.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5224	1892

prune116.0ms (2.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	4	99

Merged error: 0.0b

Counts

99 → 4

Compiler

Compiled 1567 to 1208 computations (22.9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 (pow.f64 eps 5) -2/5) (.f64 (pow.f64 eps 3) -2/3))
0.1b	(*.f64 (pow.f64 eps 5) -2/5)
0.2b	(*.f64 (pow.f64 eps 3) -2/3)

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_1109`
19×	`associate-l_binary64_1031`
13×	`add-exp-log_binary64_1123`
10×	`*-un-lft-identity_binary64_1088` `add-cube-cbrt_binary64_1120`
8×	`unpow-prod-down_binary64_1164`
7×	`add-cbrt-cube_binary64_1121` `unswap-sqr_binary64_1056`
6×	`associate-r_binary64_1030` `prod-exp_binary64_1134`
5×	`add-log-exp_binary64_1124`
4×	`cube-prod_binary64_1113` `sqr-pow_binary64_1060`
3×	`pow1_binary64_1146`
2×	`*-commutative_binary64_1021` `cbrt-unprod_binary64_1118` `pow-exp_binary64_1153` `pow-to-exp_binary64_1154`
1×	`unpow3_binary64_1151` `cube-mult_binary64_1115` `sum-log_binary64_1176` `+-commutative_binary64_1020` `flip-+_binary64_1062` `flip3-+_binary64_1091`

Counts

3 → 67

Calls

3 calls:

7.0ms	(*.f64 (pow.f64 eps 3) -2/3)
6.0ms	(+.f64 (.f64 (pow.f64 eps 5) -2/5) (.f64 (pow.f64 eps 3) -2/3))
5.0ms	(*.f64 (pow.f64 eps 5) -2/5)

series311.0ms (6.3%)

Counts

3 → 9

Calls

3 calls:

193.0ms	(+.f64 (.f64 (pow.f64 eps 5) -2/5) (.f64 (pow.f64 eps 3) -2/3))
68.0ms	(*.f64 (pow.f64 eps 5) -2/5)
49.0ms	(*.f64 (pow.f64 eps 3) -2/3)

simplify65.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4941	890
1	4941	890

prune93.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	76	4	80

Merged error: 0.0b

Counts

80 → 4

Compiler

Compiled 1551 to 1240 computations (20.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
0.0b	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
6.1b	(log.f64 (sqrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps))))
6.1b	(log.f64 (sqrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps))))

rewrite69.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

158×	`*-un-lft-identity_binary64_1088`
106×	`add-sqr-sqrt_binary64_1109`
96×	`times-frac_binary64_1094`
66×	`log-prod_binary64_1171`
60×	`sqrt-prod_binary64_1103`
52×	`add-cube-cbrt_binary64_1120`
36×	`difference-of-squares_binary64_1057`
26×	`distribute-lft-out_binary64_1041`
18×	`distribute-lft-out--_binary64_1042`
12×	`associate-/l*_binary64_1035`
10×	`add-exp-log_binary64_1123`
8×	`add-cbrt-cube_binary64_1121` `associate-/r*_binary64_1034` `associate-/r/_binary64_1036` `pow1_binary64_1146`
6×	`log-pow_binary64_1174`
4×	`associate-/l/_binary64_1037` `flip-+_binary64_1062` `add-log-exp_binary64_1124` `flip3-+_binary64_1091` `div-inv_binary64_1085`
2×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `rem-log-exp_binary64_1126` `flip3--_binary64_1092` `flip--_binary64_1063` `div-exp_binary64_1136` `div-sub_binary64_1093` `sqrt-div_binary64_1104` `log-div_binary64_1172` `cbrt-undiv_binary64_1119` `sqrt-pow1_binary64_1105` `pow1/2_binary64_1165`

Counts

4 → 192

Calls

4 calls:

12.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
11.0ms	(log.f64 (sqrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps))))
11.0ms	(log.f64 (sqrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps))))
10.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))

series217.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

86.0ms	(log.f64 (sqrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps))))
79.0ms	(log.f64 (sqrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps))))
29.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
24.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))

simplify87.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4930	4268
1	4930	4268

prune326.0ms (6.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	204	4	208

Merged error: 0.0b

Counts

208 → 4

Compiler

Compiled 5495 to 4342 computations (21% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 eps))
0.0b	(/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps))
6.1b	(log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps)))
6.2b	(log.f64 (sqrt.f64 (-.f64 1 eps)))

rewrite53.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`*-un-lft-identity_binary64_1088`
79×	`add-sqr-sqrt_binary64_1109`
72×	`times-frac_binary64_1094`
66×	`sqrt-prod_binary64_1103`
51×	`log-prod_binary64_1171`
45×	`add-cube-cbrt_binary64_1120`
22×	`difference-of-squares_binary64_1057`
19×	`distribute-lft-out_binary64_1041`
11×	`distribute-lft-out--_binary64_1042`
10×	`add-exp-log_binary64_1123`
9×	`associate-/l*_binary64_1035`
8×	`pow1_binary64_1146`
6×	`add-cbrt-cube_binary64_1121` `sqrt-div_binary64_1104`
4×	`log-pow_binary64_1174` `associate-/r*_binary64_1034` `associate-/r/_binary64_1036` `add-log-exp_binary64_1124`
3×	`rem-log-exp_binary64_1126` `flip3--_binary64_1092` `flip--_binary64_1063` `log-div_binary64_1172`
2×	`associate-/l/_binary64_1037` `div-exp_binary64_1136` `flip-+_binary64_1062` `flip3-+_binary64_1091` `sqrt-pow1_binary64_1105` `div-inv_binary64_1085` `pow1/2_binary64_1165`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `rem-sqrt-square_binary64_1101` `cbrt-undiv_binary64_1119`

Counts

4 → 158

Calls

4 calls:

10.0ms	(/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps))
10.0ms	(log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps)))
5.0ms	(log.f64 (sqrt.f64 (-.f64 1 eps)))
4.0ms	(sqrt.f64 (-.f64 1 eps))

series188.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(log.f64 (/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps)))
49.0ms	(/.f64 (sqrt.f64 (-.f64 1 eps)) (+.f64 1 eps))
42.0ms	(log.f64 (sqrt.f64 (-.f64 1 eps)))
26.0ms	(sqrt.f64 (-.f64 1 eps))

simplify91.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4960	3707
1	4960	3707

prune246.0ms (5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	170	4	174

Merged error: 0.0b

Counts

174 → 4

Compiler

Compiled 3978 to 3149 computations (20.8% saved)

regimes24.0ms (0.5%)

Compiler: Compiled 174 to 148 computations (14.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	22
1	19	22

end0.0ms (0%)

sample2.4s (48.2%)

Algorithm

1×

intervals

Results

1.4s	3942×	body	1024	valid
387.0ms	2061×	body	512	valid
207.0ms	393×	body	2048	valid
106.0ms	987×	body	256	valid
31.0ms	617×	body	128	valid

Compiler

Compiled 118 to 102 computations (13.6% saved)

Details

analyze4.0ms (0.1%)

sample71.0ms (1.4%)

simplify366.0ms (7.4%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite28.0ms (0.6%)

series85.0ms (1.7%)

simplify73.0ms (1.5%)

prune116.0ms (2.3%)

localize9.0ms (0.2%)

rewrite24.0ms (0.5%)

series311.0ms (6.3%)

simplify65.0ms (1.3%)

prune93.0ms (1.9%)

localize8.0ms (0.2%)

rewrite69.0ms (1.4%)

series217.0ms (4.4%)

simplify87.0ms (1.8%)

prune326.0ms (6.6%)

localize9.0ms (0.2%)

rewrite53.0ms (1.1%)

series188.0ms (3.8%)

simplify91.0ms (1.8%)

prune246.0ms (5%)

regimes24.0ms (0.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.4s (48.2%)

Profiling