Details

analyze5.0ms (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 13 to 12 computations (7.7% saved)

sample84.0ms (1.2%)

Algorithm

1×

intervals

Results

49.0ms	126×	body	1024	valid
17.0ms	78×	body	512	valid
8.0ms	13×	body	2048	valid
3.0ms	24×	body	256	valid
1.0ms	15×	body	128	valid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify186.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	450	15
1	450	15

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 59.5b

Counts

2 → 1

Compiler

Compiled 42 to 38 computations (9.5% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 1 x) (-.f64 1 x))
5.2b	(log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64_1111`
52×	`add-sqr-sqrt_binary64_1133`
48×	`times-frac_binary64_1117`
30×	`log-prod_binary64_1197`
25×	`add-cube-cbrt_binary64_1146`
18×	`difference-of-squares_binary64_1080`
13×	`distribute-lft-out_binary64_1062`
9×	`distribute-lft-out--_binary64_1063`
7×	`add-exp-log_binary64_1149`
6×	`associate-/r*_binary64_1055`
4×	`add-cbrt-cube_binary64_1147` `associate-/l*_binary64_1056` `associate-/r/_binary64_1057`
3×	`pow1_binary64_1172`
2×	`div-inv_binary64_1108` `flip3--_binary64_1115` `associate-/l/_binary64_1058` `div-exp_binary64_1162` `add-log-exp_binary64_1150` `rem-log-exp_binary64_1152` `flip--_binary64_1086`
1×	`flip-+_binary64_1085` `frac-2neg_binary64_1122` `flip3-+_binary64_1114` `log-pow_binary64_1200` `cbrt-undiv_binary64_1145` `log-div_binary64_1198` `clear-num_binary64_1110`

Counts

2 → 91

Calls

2 calls:

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

series87.0ms (1.2%)

Counts

2 → 6

Calls

2 calls:

59.0ms	(log.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))
27.0ms	(/.f64 (+.f64 1 x) (-.f64 1 x))

simplify87.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5296	1898

prune178.0ms (2.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	2	98

Merged error: 0.0b

Counts

98 → 2

Compiler

Compiled 2692 to 2223 computations (17.4% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 (pow.f64 x 3) 2/3) (.f64 2/5 (pow.f64 x 5)))
0.1b	(*.f64 2/5 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 2/3)

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_1133`
15×	`associate-l_binary64_1052`
13×	`add-exp-log_binary64_1149`
10×	`-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146` `associate-r*_binary64_1051`
8×	`unpow-prod-down_binary64_1190`
7×	`add-cbrt-cube_binary64_1147` `unswap-sqr_binary64_1079`
6×	`prod-exp_binary64_1160`
5×	`add-log-exp_binary64_1150`
4×	`cube-prod_binary64_1139` `sqr-pow_binary64_1083`
3×	`pow1_binary64_1172`
2×	`*-commutative_binary64_1042` `cbrt-unprod_binary64_1144` `pow-exp_binary64_1179` `pow-to-exp_binary64_1180`
1×	`cube-mult_binary64_1141` `flip-+_binary64_1085` `flip3-+_binary64_1114` `+-commutative_binary64_1041` `unpow3_binary64_1177` `sum-log_binary64_1202`

Counts

3 → 67

Calls

3 calls:

7.0ms	(*.f64 (pow.f64 x 3) 2/3)
6.0ms	(*.f64 2/5 (pow.f64 x 5))
6.0ms	(+.f64 (.f64 (pow.f64 x 3) 2/3) (.f64 2/5 (pow.f64 x 5)))

series289.0ms (4.2%)

Counts

3 → 9

Calls

3 calls:

180.0ms	(+.f64 (.f64 (pow.f64 x 3) 2/3) (.f64 2/5 (pow.f64 x 5)))
58.0ms	(*.f64 2/5 (pow.f64 x 5))
51.0ms	(*.f64 (pow.f64 x 3) 2/3)

simplify95.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4838	889
1	4838	889

prune89.0ms (1.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	76	2	78

Merged error: 0.0b

Counts

78 → 2

Compiler

Compiled 1669 to 1213 computations (27.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 (log.f64 (cbrt.f64 (-.f64 1 x))) -2) (log.f64 (/.f64 (+.f64 1 x) (cbrt.f64 (-.f64 1 x)))))
0.0b	(/.f64 (+.f64 1 x) (cbrt.f64 (-.f64 1 x)))
5.3b	(log.f64 (/.f64 (+.f64 1 x) (cbrt.f64 (-.f64 1 x))))
5.4b	(log.f64 (cbrt.f64 (-.f64 1 x)))

rewrite67.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

160×	`*-un-lft-identity_binary64_1111`
108×	`times-frac_binary64_1117`
104×	`add-sqr-sqrt_binary64_1133`
93×	`log-prod_binary64_1197`
84×	`cbrt-prod_binary64_1142`
62×	`add-cube-cbrt_binary64_1146`
42×	`associate-+r+_binary64_1043`
28×	`difference-of-squares_binary64_1080` `distribute-lft-out_binary64_1062`
14×	`distribute-lft-out--_binary64_1063`
10×	`add-exp-log_binary64_1149`
9×	`associate-/r*_binary64_1055`
8×	`cbrt-div_binary64_1143`
6×	`pow1_binary64_1172` `associate-/r/_binary64_1057`
5×	`add-cbrt-cube_binary64_1147` `add-log-exp_binary64_1150`
4×	`flip3--_binary64_1115` `associate-/l*_binary64_1056` `log-div_binary64_1198` `flip--_binary64_1086`
3×	`div-inv_binary64_1108` `log-pow_binary64_1200` `rem-log-exp_binary64_1152`
2×	`flip-+_binary64_1085` `associate-/l/_binary64_1058` `flip3-+_binary64_1114` `div-exp_binary64_1162`
1×	`pow1/3_binary64_1193` `frac-2neg_binary64_1122` `+-commutative_binary64_1041` `cbrt-undiv_binary64_1145` `sum-log_binary64_1202` `associate-+r-_binary64_1045` `clear-num_binary64_1110`

Counts

4 → 193

Calls

4 calls:

17.0ms	(+.f64 (*.f64 (log.f64 (cbrt.f64 (-.f64 1 x))) -2) (log.f64 (/.f64 (+.f64 1 x) (cbrt.f64 (-.f64 1 x)))))
10.0ms	(log.f64 (/.f64 (+.f64 1 x) (cbrt.f64 (-.f64 1 x))))
10.0ms	(/.f64 (+.f64 1 x) (cbrt.f64 (-.f64 1 x)))
5.0ms	(log.f64 (cbrt.f64 (-.f64 1 x)))

series444.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

258.0ms	(+.f64 (*.f64 (log.f64 (cbrt.f64 (-.f64 1 x))) -2) (log.f64 (/.f64 (+.f64 1 x) (cbrt.f64 (-.f64 1 x)))))
72.0ms	(log.f64 (/.f64 (+.f64 1 x) (cbrt.f64 (-.f64 1 x))))
59.0ms	(log.f64 (cbrt.f64 (-.f64 1 x)))
55.0ms	(/.f64 (+.f64 1 x) (cbrt.f64 (-.f64 1 x)))

simplify107.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4921	4956
1	4921	4956

prune409.0ms (5.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	205	2	207

Merged error: 0.0b

Counts

207 → 2

Compiler

Compiled 5978 to 5018 computations (16.1% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

4.1b	(log.f64 (/.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (-.f64 1 (sqrt.f64 x)))))
4.1b	(log.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 x))))
5.2b	(log.f64 (cbrt.f64 (+.f64 1 x)))
5.4b	(log.f64 (cbrt.f64 (-.f64 1 x)))

rewrite61.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

126×	`cbrt-prod_binary64_1142`
116×	`*-un-lft-identity_binary64_1111`
114×	`log-prod_binary64_1197`
102×	`add-sqr-sqrt_binary64_1133`
84×	`times-frac_binary64_1117`
49×	`add-cube-cbrt_binary64_1146`
30×	`difference-of-squares_binary64_1080`
22×	`sqrt-prod_binary64_1127`
15×	`distribute-lft-out_binary64_1062` `distribute-lft-out--_binary64_1063`
10×	`add-exp-log_binary64_1149`
8×	`pow1_binary64_1172` `cbrt-div_binary64_1143`
7×	`log-pow_binary64_1200` `log-div_binary64_1198`
5×	`rem-log-exp_binary64_1152`
4×	`add-cbrt-cube_binary64_1147` `add-log-exp_binary64_1150`
3×	`pow1/3_binary64_1193`
2×	`flip-+_binary64_1085` `flip3--_binary64_1115` `flip3-+_binary64_1114` `flip--_binary64_1086` `associate-/r/_binary64_1057`
1×	`div-inv_binary64_1108` `div-exp_binary64_1162`

Counts

4 → 161

Calls

4 calls:

18.0ms	(log.f64 (/.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (-.f64 1 (sqrt.f64 x)))))
6.0ms	(log.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 x))))
5.0ms	(log.f64 (cbrt.f64 (-.f64 1 x)))
5.0ms	(log.f64 (cbrt.f64 (+.f64 1 x)))

series1.2s (17.2%)

Counts

4 → 12

Calls

4 calls:

980.0ms	(log.f64 (/.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (-.f64 1 (sqrt.f64 x)))))
114.0ms	(log.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 x))))
54.0ms	(log.f64 (cbrt.f64 (-.f64 1 x)))
51.0ms	(log.f64 (cbrt.f64 (+.f64 1 x)))

simplify143.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4923	5867
1	4923	5867

prune635.0ms (9.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	173	2	175

Merged error: 0b

Counts

175 → 2

Compiler

Compiled 8728 to 6942 computations (20.5% saved)

regimes11.0ms (0.2%)

Compiler: Compiled 57 to 49 computations (14% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	25
1	20	25

end0.0ms (0%)

sample2.7s (38.3%)

Algorithm

1×

intervals

Results

1.6s	3973×	body	1024	valid
445.0ms	2020×	body	512	valid
228.0ms	392×	body	2048	valid
132.0ms	1015×	body	256	valid
39.0ms	600×	body	128	valid

Compiler

Compiled 85 to 74 computations (12.9% saved)

Details

analyze5.0ms (0.1%)

sample84.0ms (1.2%)

simplify186.0ms (2.7%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

rewrite27.0ms (0.4%)

series87.0ms (1.2%)

simplify87.0ms (1.3%)

prune178.0ms (2.6%)

localize11.0ms (0.2%)

rewrite26.0ms (0.4%)

series289.0ms (4.2%)

simplify95.0ms (1.4%)

prune89.0ms (1.3%)

localize14.0ms (0.2%)

rewrite67.0ms (1%)

series444.0ms (6.4%)

simplify107.0ms (1.5%)

prune409.0ms (5.9%)

localize24.0ms (0.3%)

rewrite61.0ms (0.9%)

series1.2s (17.2%)

simplify143.0ms (2.1%)

prune635.0ms (9.1%)

regimes11.0ms (0.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (38.3%)

Profiling