Details

analyze466.0ms (5.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	74.9%	25.1%	5
0%	74.9%	25.1%	6
0%	74.9%	25.1%	7
6.2%	56.2%	37.6%	8
7.8%	53%	39.2%	9
10.9%	45.6%	43.4%	10
18.3%	31.4%	50.3%	11
19.1%	29.5%	51.3%	12
21.4%	24.8%	53.8%	13
25.8%	16.7%	57.5%	14

Compiler

Compiled 25 to 21 computations (16% saved)

sample36.0ms (0.4%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
5.0ms	40×	body	128	invalid
1.0ms	21×	body	128	nan

Compiler

Compiled 49 to 44 computations (10.2% saved)

simplify432.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (271.0ms)

Iter	Nodes	Cost
0	5077	36

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 5.5b

Counts

2 → 1

Compiler

Compiled 48 to 40 computations (16.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
0.1b	(*.f64 (-.f64 x 1/2) (log.f64 x))
0.2b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
5.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite53.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_15237` `*-un-lft-identity_binary64_15215`
22×	`add-cube-cbrt_binary64_15250`
18×	`log-prod_binary64_15301`
12×	`associate--l+_binary64_15152`
11×	`add-log-exp_binary64_15254`
10×	`associate-+l+_binary64_15148`
9×	`distribute-rgt-in_binary64_15165` `times-frac_binary64_15221` `distribute-lft-in_binary64_15164`
8×	`add-cbrt-cube_binary64_15251` `add-exp-log_binary64_15253`
7×	`pow1_binary64_15276`
6×	`cancel-sign-sub-inv_binary64_15181`
5×	`associate-l_binary64_15156`
4×	`associate-r_binary64_15155`
3×	`associate-/l_binary64_15160` `associate-/r_binary64_15159`
2×	`flip-+_binary64_15189` `sub-neg_binary64_15208` `associate-*l/_binary64_15158` `flip3--_binary64_15219` `flip--_binary64_15190` `associate-/l/_binary64_15162` `flip3-+_binary64_15218` `sum-log_binary64_15306` `diff-log_binary64_15307`
1×	`distribute-lft-out_binary64_15166` `associate-+l-_binary64_15150` `unswap-sqr_binary64_15183` `frac-2neg_binary64_15226` `cbrt-unprod_binary64_15248` `div-inv_binary64_15212` `clear-num_binary64_15214` `+-commutative_binary64_15145` `pow-prod-down_binary64_15286` `*-commutative_binary64_15146` `log-pow_binary64_15304` `prod-exp_binary64_15264` `cbrt-undiv_binary64_15249` `difference-of-squares_binary64_15184` `distribute-lft-out--_binary64_15167` `div-exp_binary64_15266`

Counts

4 → 102

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
12.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
8.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
8.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))

series937.0ms (10.2%)

Counts

4 → 12

Calls

4 calls:

307.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
307.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
174.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
148.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify75.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4940	2164
1	4940	2164

prune803.0ms (8.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	104	10	114
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	11	115

Merged error: 3.3b

Counts

115 → 11

Compiler

Compiled 16532 to 12652 computations (23.5% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2))
0.1b	(*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x)))
0.1b	(+.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)) 2069265617858471/2251799813685248)
5.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite68.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_15237`
28×	`*-un-lft-identity_binary64_15215`
22×	`add-cube-cbrt_binary64_15250`
13×	`add-log-exp_binary64_15254`
12×	`pow1_binary64_15276` `log-prod_binary64_15301`
11×	`associate-l_binary64_15156` `associate-r_binary64_15155`
10×	`add-cbrt-cube_binary64_15251` `distribute-rgt-in_binary64_15165` `distribute-lft-in_binary64_15164` `add-exp-log_binary64_15253`
9×	`times-frac_binary64_15221`
6×	`cancel-sign-sub-inv_binary64_15181` `log-pow_binary64_15304` `sqrt-prod_binary64_15231`
5×	`sum-log_binary64_15306`
3×	`associate-/l_binary64_15160` `associate-/r_binary64_15159`
2×	`flip-+_binary64_15189` `sub-neg_binary64_15208` `pow1/2_binary64_15295` `associate-l/_binary64_15158` `flip3--_binary64_15219` `flip--_binary64_15190` `unswap-sqr_binary64_15183` `cbrt-unprod_binary64_15248` `associate-r/_binary64_15157` `associate-/l/_binary64_15162` `flip3-+_binary64_15218` `pow-prod-down_binary64_15286` `*-commutative_binary64_15146` `prod-exp_binary64_15264` `difference-of-squares_binary64_15184` `distribute-lft-out--_binary64_15167` `sqrt-pow1_binary64_15233`
1×	`distribute-lft-out_binary64_15166` `associate-+l-_binary64_15150` `associate-+r-_binary64_15149` `associate-+l+_binary64_15148` `frac-2neg_binary64_15226` `div-inv_binary64_15212` `clear-num_binary64_15214` `+-commutative_binary64_15145` `cbrt-undiv_binary64_15249` `diff-log_binary64_15307` `div-exp_binary64_15266`

Counts

4 → 115

Calls

4 calls:

18.0ms	(+.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)) 2069265617858471/2251799813685248)
13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
11.0ms	(*.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2))
10.0ms	(*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x)))

series333.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

144.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
88.0ms	(+.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)) 2069265617858471/2251799813685248)
51.0ms	(*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x)))
51.0ms	(*.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2))

simplify84.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4969	2848
1	4969	2848

prune260.0ms (2.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	127	11	138

Merged error: 3.3b

Counts

138 → 11

Compiler

Compiled 5478 to 3457 computations (36.9% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 (-.f64 x 1/2) (.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 1/2) (log.f64 (cbrt.f64 x))))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
5.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite48.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`log-prod_binary64_15301`
30×	`distribute-rgt-in_binary64_15165` `distribute-lft-in_binary64_15164`
26×	`add-sqr-sqrt_binary64_15237` `*-un-lft-identity_binary64_15215` `add-cube-cbrt_binary64_15250`
24×	`cbrt-prod_binary64_15246` `associate-+l+_binary64_15148`
12×	`associate-+r+_binary64_15147`
9×	`times-frac_binary64_15221`
8×	`associate-*l/_binary64_15158`
6×	`add-cbrt-cube_binary64_15251` `add-log-exp_binary64_15254` `add-exp-log_binary64_15253`
4×	`flip3--_binary64_15219` `flip--_binary64_15190` `pow1_binary64_15276` `frac-add_binary64_15223`
3×	`associate-/l_binary64_15160` `associate-/r_binary64_15159`
2×	`flip-+_binary64_15189` `pow1/3_binary64_15297` `associate-/l/_binary64_15162` `flip3-+_binary64_15218`
1×	`distribute-lft-out_binary64_15166` `frac-2neg_binary64_15226` `div-inv_binary64_15212` `clear-num_binary64_15214` `+-commutative_binary64_15145` `sum-log_binary64_15306` `cbrt-undiv_binary64_15249` `div-exp_binary64_15266`

Counts

4 → 103

Calls

4 calls:

17.0ms	(+.f64 (.f64 (-.f64 x 1/2) (.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 1/2) (log.f64 (cbrt.f64 x))))
13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series1.2s (13.1%)

Counts

4 → 12

Calls

4 calls:

746.0ms	(+.f64 (.f64 (-.f64 x 1/2) (.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 1/2) (log.f64 (cbrt.f64 x))))
166.0ms	(cbrt.f64 x)
148.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
147.0ms	(cbrt.f64 x)

simplify87.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4885	2171
1	4885	2171

prune282.0ms (3.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	115	11	126

Merged error: 3.3b

Counts

126 → 11

Compiler

Compiled 5720 to 3850 computations (32.7% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 x)) (cbrt.f64 -1))) (+.f64 -3/2 (*.f64 x 3))) x)
0.3b	(.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 x)) (cbrt.f64 -1))) (+.f64 -3/2 (*.f64 x 3)))
0.6b	(cbrt.f64 (neg.f64 x))
5.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite47.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_15237`
18×	`*-un-lft-identity_binary64_15215` `add-cube-cbrt_binary64_15250`
10×	`cbrt-prod_binary64_15246`
9×	`pow1_binary64_15276` `times-frac_binary64_15221`
8×	`add-cbrt-cube_binary64_15251` `add-exp-log_binary64_15253`
6×	`associate-l_binary64_15156` `add-log-exp_binary64_15254`
3×	`associate-/l_binary64_15160` `pow1/3_binary64_15297` `associate-r_binary64_15155` `cancel-sign-sub-inv_binary64_15181` `distribute-lft-neg-in_binary64_15172` `pow-prod-down_binary64_15286` `log-pow_binary64_15304` `distribute-rgt-neg-in_binary64_15173` `associate-/r_binary64_15159`
2×	`flip-+_binary64_15189` `associate-*r/_binary64_15157` `associate-/l/_binary64_15162` `distribute-rgt-in_binary64_15165` `associate--l+_binary64_15152` `flip3-+_binary64_15218` `distribute-lft-in_binary64_15164`
1×	`sub-neg_binary64_15208` `neg-mul-1_binary64_15211` `flip3--_binary64_15219` `flip--_binary64_15190` `unswap-sqr_binary64_15183` `frac-2neg_binary64_15226` `cbrt-unprod_binary64_15248` `div-inv_binary64_15212` `clear-num_binary64_15214` `*-commutative_binary64_15146` `prod-exp_binary64_15264` `cbrt-undiv_binary64_15249` `diff-log_binary64_15307` `div-exp_binary64_15266`

Counts

4 → 88

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
11.0ms	(.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 x)) (cbrt.f64 -1))) (+.f64 -3/2 (*.f64 x 3)))
10.0ms	(-.f64 (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 x)) (cbrt.f64 -1))) (+.f64 -3/2 (*.f64 x 3))) x)
2.0ms	(cbrt.f64 (neg.f64 x))

series1.8s (19.7%)

Counts

4 → 12

Calls

4 calls:

950.0ms	(-.f64 (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 x)) (cbrt.f64 -1))) (+.f64 -3/2 (*.f64 x 3))) x)
548.0ms	(.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 x)) (cbrt.f64 -1))) (+.f64 -3/2 (*.f64 x 3)))
175.0ms	(cbrt.f64 (neg.f64 x))
139.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4956	2272
1	4956	2272

prune348.0ms (3.8%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	100	11	111

Merged error: 3.3b

Counts

111 → 11

Compiler

Compiled 4236 to 3081 computations (27.3% saved)

regimes300.0ms (3.3%)

Compiler: Compiled 3065 to 2517 computations (17.9% saved)

bsearch1.0ms (0%)

Compiler: Compiled 9 to 9 computations (0% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	99	113
1	99	113

end0.0ms (0%)

sample1.4s (14.8%)

Algorithm

1×

intervals

Results

602.0ms	8000×	body	128	valid
98.0ms	1277×	body	128	invalid
45.0ms	704×	body	128	nan

Compiler

Compiled 483 to 389 computations (19.5% saved)

Details

analyze466.0ms (5.1%)

sample36.0ms (0.4%)

simplify432.0ms (4.7%)

prune6.0ms (0.1%)

localize17.0ms (0.2%)

rewrite53.0ms (0.6%)

series937.0ms (10.2%)

simplify75.0ms (0.8%)

prune803.0ms (8.7%)

localize22.0ms (0.2%)

rewrite68.0ms (0.7%)

series333.0ms (3.6%)

simplify84.0ms (0.9%)

prune260.0ms (2.8%)

localize23.0ms (0.3%)

rewrite48.0ms (0.5%)

series1.2s (13.1%)

simplify87.0ms (0.9%)

prune282.0ms (3.1%)

localize23.0ms (0.3%)

rewrite47.0ms (0.5%)

series1.8s (19.7%)

simplify69.0ms (0.8%)

prune348.0ms (3.8%)

regimes300.0ms (3.3%)

bsearch1.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.4s (14.8%)

Profiling