Details

analyze783.0ms (13.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
3%	46.9%	50%	13
3.1%	46.8%	50%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample65.0ms (1.1%)

Algorithm

1×

intervals

Results

37.0ms	127×	body	2048	valid
14.0ms	68×	body	1024	valid
3.0ms	24×	body	512	valid
2.0ms	21×	body	256	valid
1.0ms	16×	body	128	valid

Compiler

Compiled 29 to 22 computations (24.1% saved)

simplify169.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4955	21
1	4955	21

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

Error

0.7b

Counts

2 → 1

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 1 (.f64 5 (.f64 v v)))
0.0b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
0.1b	(.f64 5 (.f64 v v))
0.7b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_2146`
20×	`*-un-lft-identity_binary64_2124`
18×	`times-frac_binary64_2130`
16×	`add-cube-cbrt_binary64_2159`
11×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
9×	`pow1_binary64_2185`
8×	`difference-of-squares_binary64_2093`
6×	`associate-/r*_binary64_2068` `add-log-exp_binary64_2163`
4×	`difference-of-sqr-1_binary64_2094`
3×	`flip--_binary64_2099` `pow-prod-down_binary64_2195` `flip3--_binary64_2128` `associate-/l_binary64_2069` `associate-l*_binary64_2065` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
2×	`associate-/r/_binary64_2070` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `cancel-sign-sub-inv_binary64_2090` `unswap-sqr_binary64_2092` `-commutative_binary64_2055` `acos-asin_binary64_2305` `diff-log_binary64_2216` `sub-neg_binary64_2117` `associate-r*_binary64_2064` `div-sub_binary64_2129` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 83

Calls

4 calls:

9.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
6.0ms	(.f64 5 (.f64 v v))
3.0ms	(-.f64 1 (.f64 5 (.f64 v v)))
1.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

series94.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(-.f64 1 (.f64 5 (.f64 v v)))
30.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
17.0ms	(.f64 5 (.f64 v v))
14.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

simplify69.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5495	1994

prune116.0ms (2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	3	96

Error

0.7b

Counts

96 → 3

Compiler

Compiled 2054 to 1320 computations (35.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1))
0.1b	(*.f64 125 (pow.f64 v 6))
0.7b	(acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1)))
19.9b	(cbrt.f64 (*.f64 125 (pow.f64 v 6)))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64_2146`
49×	`*-un-lft-identity_binary64_2124`
36×	`times-frac_binary64_2130`
28×	`difference-of-squares_binary64_2093`
21×	`add-cube-cbrt_binary64_2159`
11×	`add-exp-log_binary64_2162`
8×	`add-cbrt-cube_binary64_2160`
7×	`distribute-lft-out--_binary64_2076` `associate-r_binary64_2064` `difference-of-sqr-1_binary64_2094`
6×	`associate-/l_binary64_2069` `associate-/r_binary64_2068`
4×	`unpow-prod-down_binary64_2203` `pow1_binary64_2185` `add-log-exp_binary64_2163`
3×	`unswap-sqr_binary64_2092` `associate-l_binary64_2065` `prod-exp_binary64_2173`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r/_binary64_2070` `sqr-pow_binary64_2096` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `pow-exp_binary64_2192` `*-commutative_binary64_2055` `acos-asin_binary64_2305` `pow1/3_binary64_2206` `cbrt-prod_binary64_2155` `pow-to-exp_binary64_2193` `div-sub_binary64_2129` `div-inv_binary64_2121` `div-exp_binary64_2175` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`

Counts

4 → 107

Calls

4 calls:

11.0ms	(/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1))
6.0ms	(*.f64 125 (pow.f64 v 6))
3.0ms	(cbrt.f64 (*.f64 125 (pow.f64 v 6)))
1.0ms	(acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1)))

series115.0ms (2%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1))
28.0ms	(*.f64 125 (pow.f64 v 6))
28.0ms	(cbrt.f64 (*.f64 125 (pow.f64 v 6)))
13.0ms	(acos.f64 (/.f64 (-.f64 1 (cbrt.f64 (.f64 125 (pow.f64 v 6)))) (-.f64 (.f64 v v) 1)))

simplify69.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5422	2982

prune158.0ms (2.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	119	3	122

Error

0.7b

Counts

122 → 3

Compiler

Compiled 2841 to 2193 computations (22.8% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 v (.f64 (+.f64 (pow.f64 v 3) v) 4)) -1)
0.0b	(+.f64 (pow.f64 v 3) v)
0.7b	(acos.f64 (+.f64 (.f64 v (.f64 (+.f64 (pow.f64 v 3) v) 4)) -1))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-log-exp_binary64_2163`
6×	`*-un-lft-identity_binary64_2124`
3×	`pow1_binary64_2185` `add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
2×	`unpow3_binary64_2190` `sum-log_binary64_2215` `+-commutative_binary64_2054` `flip3-+_binary64_2127` `flip-+_binary64_2098`
1×	`acos-asin_binary64_2305` `distribute-lft-out_binary64_2075` `distribute-rgt-out_binary64_2077` `distribute-lft1-in_binary64_2079`

Counts

3 → 33

Calls

3 calls:

12.0ms	(+.f64 (.f64 v (.f64 (+.f64 (pow.f64 v 3) v) 4)) -1)
7.0ms	(+.f64 (pow.f64 v 3) v)
2.0ms	(acos.f64 (+.f64 (.f64 v (.f64 (+.f64 (pow.f64 v 3) v) 4)) -1))

series72.0ms (1.3%)

Counts

3 → 9

Calls

3 calls:

37.0ms	(+.f64 (pow.f64 v 3) v)
24.0ms	(+.f64 (.f64 v (.f64 (+.f64 (pow.f64 v 3) v) 4)) -1)
12.0ms	(acos.f64 (+.f64 (.f64 v (.f64 (+.f64 (pow.f64 v 3) v) 4)) -1))

simplify73.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5085	713

prune43.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	42	3	45

Error

0.7b

Counts

45 → 3

Compiler

Compiled 764 to 582 computations (23.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1))) (cbrt.f64 (acos.f64 (+.f64 (.f64 v (*.f64 (+.f64 v (pow.f64 v 3)) 4)) -1))))
1.0b	(cbrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1)))
1.0b	(cbrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1)))
1.0b	(cbrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1)))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_2155`
23×	`add-sqr-sqrt_binary64_2146`
15×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
11×	`pow1_binary64_2185`
9×	`pow1/3_binary64_2206`
6×	`swap-sqr_binary64_2091` `associate-l_binary64_2065` `associate-r_binary64_2064` `add-exp-log_binary64_2162`
4×	`unswap-sqr_binary64_2092` `add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160`
2×	`pow-prod-down_binary64_2195` `pow-prod-up_binary64_2194` `pow-sqr_binary64_2097`
1×	`*-commutative_binary64_2055` `prod-exp_binary64_2173` `pow-plus_binary64_2187` `pow2_binary64_2205` `cbrt-unprod_binary64_2157`

Counts

4 → 73

Calls

4 calls:

6.0ms	(.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1))) (cbrt.f64 (acos.f64 (+.f64 (.f64 v (*.f64 (+.f64 v (pow.f64 v 3)) 4)) -1))))
1.0ms	(cbrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1)))
1.0ms	(cbrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1)))
1.0ms	(cbrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1)))

series814.0ms (14.1%)

Counts

4 → 12

Calls

4 calls:

255.0ms	(.f64 (cbrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1))) (cbrt.f64 (acos.f64 (+.f64 (.f64 v (*.f64 (+.f64 v (pow.f64 v 3)) 4)) -1))))
192.0ms	(cbrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1)))
189.0ms	(cbrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1)))
177.0ms	(cbrt.f64 (acos.f64 (+.f64 (.f64 v (.f64 (+.f64 v (pow.f64 v 3)) 4)) -1)))

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4907	2202
1	4907	2202

prune183.0ms (3.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	84	4	88

Error

0.7b

Counts

88 → 4

Compiler

Compiled 3725 to 2949 computations (20.8% saved)

regimes186.0ms (3.2%)

Accuracy

Total 0.0b remaining (6.5%)

Threshold costs 0.0b (6.5%)

Compiler

Compiled 2743 to 2149 computations (21.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	25
1	35	25

end0.0ms (0%)

sample2.5s (43.9%)

Algorithm

1×

intervals

Results

1.2s	4059×	body	2048	valid
388.0ms	1931×	body	1024	valid
138.0ms	960×	body	512	valid
51.0ms	504×	body	256	valid
30.0ms	545×	body	128	valid
0.0ms	1×	body	4096	valid
0.0ms	6×	body	128	nan

Compiler

Compiled 640 to 507 computations (20.8% saved)

Details

analyze783.0ms (13.6%)

sample65.0ms (1.1%)

simplify169.0ms (2.9%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite25.0ms (0.4%)

series94.0ms (1.6%)

simplify69.0ms (1.2%)

prune116.0ms (2%)

localize11.0ms (0.2%)

rewrite30.0ms (0.5%)

series115.0ms (2%)

simplify69.0ms (1.2%)

prune158.0ms (2.7%)

localize10.0ms (0.2%)

rewrite24.0ms (0.4%)

series72.0ms (1.3%)

simplify73.0ms (1.3%)

prune43.0ms (0.7%)

localize13.0ms (0.2%)

rewrite20.0ms (0.4%)

series814.0ms (14.1%)

simplify74.0ms (1.3%)

prune183.0ms (3.2%)

regimes186.0ms (3.2%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.5s (43.9%)

Profiling