Details

analyze1.5s (4.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4881	464
1	4881	464
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%	74.8%	25.2%	8
0%	74.8%	25.2%	9
0%	74.8%	25.2%	10
0%	74.8%	25.2%	11
0%	74.8%	25.2%	12
24.9%	49.9%	25.2%	13
24.9%	37.4%	37.7%	14

Symmetry

(sort z t)

Compiler

Compiled 20 to 20 computations (0% saved)

sample95.0ms (0.3%)

Algorithm

1×

intervals

Results

21.0ms	52×	body	1024	valid
14.0ms	30×	body	2048	valid
11.0ms	142×	body	128	valid
6.0ms	78×	body	128	nan
6.0ms	21×	body	512	valid
2.0ms	32×	body	128	invalid
2.0ms	10×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 39 to 45 computations (-15.4% saved)

simplify50.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	757	29
1	757	29

prune5.0ms (0%)

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

Error

21.9b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 z t) 3)
0.2b	(/.f64 a (*.f64 b 3))
0.3b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
25.0b	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))

rewrite263.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

20.4b

Rules

19×	`add-exp-log_binary64_18530` `add-cbrt-cube_binary64_18528`
11×	`add-cube-cbrt_binary64_18527` `add-sqr-sqrt_binary64_18514` `*-un-lft-identity_binary64_18492`
9×	`times-frac_binary64_18498` `pow1_binary64_18553`
8×	`cos-sum_binary64_18626`
7×	`cancel-sign-sub-inv_binary64_18458`
5×	`prod-exp_binary64_18541` `cbrt-unprod_binary64_18525`
4×	`add-log-exp_binary64_18531` `div-exp_binary64_18543` `cbrt-undiv_binary64_18526` `associate-/l_binary64_18437` `associate-/r_binary64_18436`
3×	`cos-diff_binary64_18629` `div-inv_binary64_18489` `pow-prod-down_binary64_18563` `associate-r_binary64_18432`
2×	`frac-2neg_binary64_18503` `clear-num_binary64_18491`
1×	`sub-neg_binary64_18485` `distribute-rgt-in_binary64_18442` `distribute-lft-in_binary64_18441` `associate-l_binary64_18433` `*-commutative_binary64_18423`

Counts

4 → 78

Calls

4 calls:

11.0ms	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))
10.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
5.0ms	(/.f64 (*.f64 z t) 3)
5.0ms	(/.f64 a (*.f64 b 3))

Compiler

Compiled 2110 to 1295 computations (38.6% saved)

series831.0ms (2.2%)

Error

16.3b

Counts

4 → 45

Calls

4 calls:

447.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
165.0ms	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))
94.0ms	(/.f64 a (*.f64 b 3))
85.0ms	(/.f64 (*.f64 z t) 3)

Compiler

Compiled 2286 to 1984 computations (13.2% saved)

simplify84.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4932	1991
1	4932	1991

prune227.0ms (0.6%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	102	21	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	21	124

Error

15.7b

Counts

124 → 21

Compiler

Compiled 2194 to 1493 computations (32% saved)

localize11.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x))) (/.f64 a (*.f64 b 3)))
0.2b	(*.f64 (cos.f64 y) (sqrt.f64 x))
0.2b	(/.f64 a (*.f64 b 3))

rewrite162.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

15.6b

Rules

14×	`add-sqr-sqrt_binary64_18514`
10×	`add-exp-log_binary64_18530` `add-cbrt-cube_binary64_18528` `add-cube-cbrt_binary64_18527` `*-un-lft-identity_binary64_18492`
7×	`cancel-sign-sub-inv_binary64_18458`
6×	`times-frac_binary64_18498` `associate-r_binary64_18432`
5×	`pow1_binary64_18553` `add-log-exp_binary64_18531`
4×	`sqrt-prod_binary64_18508`
3×	`associate-/l_binary64_18437` `associate-l*_binary64_18433`
2×	`prod-exp_binary64_18541` `div-exp_binary64_18543` `cbrt-undiv_binary64_18526` `cbrt-unprod_binary64_18525` `div-inv_binary64_18489` `unswap-sqr_binary64_18460`
1×	`frac-2neg_binary64_18503` `clear-num_binary64_18491` `associate-/r_binary64_18436` `pow-prod-down_binary64_18563` `-commutative_binary64_18423` `diff-log_binary64_18584` `flip3--_binary64_18496` `sub-neg_binary64_18485` `flip--_binary64_18467`

Counts

3 → 61

Calls

3 calls:

12.0ms	(-.f64 (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x))) (/.f64 a (*.f64 b 3)))
6.0ms	(*.f64 (cos.f64 y) (sqrt.f64 x))
5.0ms	(/.f64 a (*.f64 b 3))

Compiler

Compiled 1155 to 593 computations (48.7% saved)

series742.0ms (2%)

Error

15.5b

Counts

3 → 36

Calls

3 calls:

521.0ms	(-.f64 (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x))) (/.f64 a (*.f64 b 3)))
99.0ms	(*.f64 (cos.f64 y) (sqrt.f64 x))
94.0ms	(/.f64 a (*.f64 b 3))

Compiler

Compiled 1048 to 1053 computations (-0.5% saved)

simplify85.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4915	1348
1	4915	1348

prune171.0ms (0.5%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	80	17	97
Fresh	8	12	20
Picked	1	0	1
Done	0	0	0
Total	89	29	118

Error

15.5b

Counts

118 → 29

Compiler

Compiled 1675 to 1113 computations (33.6% saved)

localize11.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x))) (/.f64 (/.f64 a b) 3))
0.2b	(*.f64 (cos.f64 y) (sqrt.f64 x))
0.2b	(/.f64 (/.f64 a b) 3)

rewrite381.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

15.5b

Rules

141×	`times-frac_binary64_18498`
87×	`add-sqr-sqrt_binary64_18514`
83×	`add-cube-cbrt_binary64_18527` `*-un-lft-identity_binary64_18492`
43×	`cancel-sign-sub-inv_binary64_18458`
13×	`associate-/l*_binary64_18437`
10×	`add-exp-log_binary64_18530` `add-cbrt-cube_binary64_18528`
9×	`div-inv_binary64_18489`
6×	`associate-r_binary64_18432`
5×	`pow1_binary64_18553` `add-log-exp_binary64_18531`
4×	`sqrt-prod_binary64_18508`
3×	`div-exp_binary64_18543` `cbrt-undiv_binary64_18526` `associate-/r_binary64_18436` `associate-l*_binary64_18433`
2×	`unswap-sqr_binary64_18460`
1×	`frac-2neg_binary64_18503` `clear-num_binary64_18491` `associate-/l/_binary64_18439` `pow-prod-down_binary64_18563` `prod-exp_binary64_18541` `cbrt-unprod_binary64_18525` `*-commutative_binary64_18423` `diff-log_binary64_18584` `flip3--_binary64_18496` `sub-neg_binary64_18485` `flip--_binary64_18467`

Counts

3 → 146

Calls

3 calls:

17.0ms	(-.f64 (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x))) (/.f64 (/.f64 a b) 3))
8.0ms	(*.f64 (cos.f64 y) (sqrt.f64 x))
6.0ms	(/.f64 (/.f64 a b) 3)

Compiler

Compiled 3301 to 1532 computations (53.6% saved)

series748.0ms (2%)

Error

15.5b

Counts

3 → 36

Calls

3 calls:

530.0ms	(-.f64 (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x))) (/.f64 (/.f64 a b) 3))
95.0ms	(*.f64 (cos.f64 y) (sqrt.f64 x))
92.0ms	(/.f64 (/.f64 a b) 3)

Compiler

Compiled 1048 to 1048 computations (0% saved)

simplify85.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5203	3079

prune330.0ms (0.9%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	179	3	182
Fresh	3	25	28
Picked	0	1	1
Done	0	0	0
Total	182	29	211

Error

15.5b

Counts

211 → 29

Compiler

Compiled 3205 to 1731 computations (46% saved)

localize13.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x))) (*.f64 (/.f64 1 b) (/.f64 a 3)))
0.2b	(*.f64 (cos.f64 y) (sqrt.f64 x))
0.3b	(*.f64 (/.f64 1 b) (/.f64 a 3))

rewrite262.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

15.5b

Rules

41×	`add-sqr-sqrt_binary64_18514`
27×	`add-exp-log_binary64_18530`
25×	`times-frac_binary64_18498`
22×	`*-un-lft-identity_binary64_18492`
20×	`add-cube-cbrt_binary64_18527`
19×	`associate-r_binary64_18432`
17×	`add-cbrt-cube_binary64_18528`
16×	`associate-l_binary64_18433`
9×	`prod-exp_binary64_18541`
8×	`div-exp_binary64_18543` `unswap-sqr_binary64_18460`
7×	`pow1_binary64_18553`
5×	`add-log-exp_binary64_18531` `cbrt-unprod_binary64_18525`
4×	`cbrt-undiv_binary64_18526` `sqrt-prod_binary64_18508`
2×	`pow-prod-down_binary64_18563` `1-exp_binary64_18536` `rec-exp_binary64_18542` `div-inv_binary64_18489` `*-commutative_binary64_18423`
1×	`frac-times_binary64_18502` `associate-l/_binary64_18435` `associate-r/_binary64_18434` `diff-log_binary64_18584` `flip3--_binary64_18496` `sub-neg_binary64_18485` `flip--_binary64_18467` `cancel-sign-sub-inv_binary64_18458`

Counts

3 → 90

Calls

3 calls:

15.0ms	(*.f64 (/.f64 1 b) (/.f64 a 3))
7.0ms	(-.f64 (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x))) (*.f64 (/.f64 1 b) (/.f64 a 3)))
6.0ms	(*.f64 (cos.f64 y) (sqrt.f64 x))

Compiler

Compiled 1965 to 1149 computations (41.5% saved)

series762.0ms (2.1%)

Error

15.5b

Counts

3 → 36

Calls

3 calls:

541.0ms	(-.f64 (.f64 2 (.f64 (cos.f64 y) (sqrt.f64 x))) (*.f64 (/.f64 1 b) (/.f64 a 3)))
101.0ms	(*.f64 (cos.f64 y) (sqrt.f64 x))
91.0ms	(*.f64 (/.f64 1 b) (/.f64 a 3))

Compiler

Compiled 1086 to 1091 computations (-0.5% saved)

simplify86.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4975	1746
1	4975	1746

prune192.0ms (0.5%)

Pruning

29 alts after pruning (27 fresh and 2 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	4	23	27
Picked	0	1	1
Done	0	1	1
Total	126	29	155

Error

15.5b

Counts

155 → 29

Compiler

Compiled 1583 to 851 computations (46.2% saved)

regimes26.3s (71.1%)

Accuracy

Total 2.1b remaining (12.9%)

Threshold costs 0b (0%)

Compiler

Compiled 221708 to 208859 computations (5.8% saved)

bsearch212.0ms (0.6%)

Steps

Iters	Range		Point
7	1.8549468672090944e+301	1.4137416350874014e+303	1.3799911399098672e+303
6	#hash((type . real) (value . -inf))	-3.895966282501435e+307	-1.7817790742629094e+308

Compiler

Compiled 7 to 10 computations (-42.9% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	114	89
1	114	89

end14.0ms (0%)

Remove: (sort z t)
Compiler: Compiled 177 to 126 computations (28.8% saved)

sample3.3s (9%)

Algorithm

1×

intervals

Results

541.0ms	1600×	body	1024	valid
382.0ms	4658×	body	128	valid
353.0ms	729×	body	2048	valid
192.0ms	2342×	body	128	nan
168.0ms	672×	body	512	valid
84.0ms	1118×	body	128	invalid
57.0ms	340×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 817 to 752 computations (8% saved)

Details

analyze1.5s (4.1%)

sample95.0ms (0.3%)

simplify50.0ms (0.1%)

prune5.0ms (0%)

localize16.0ms (0%)

rewrite263.0ms (0.7%)

series831.0ms (2.2%)

simplify84.0ms (0.2%)

prune227.0ms (0.6%)

localize11.0ms (0%)

rewrite162.0ms (0.4%)

series742.0ms (2%)

simplify85.0ms (0.2%)

prune171.0ms (0.5%)

localize11.0ms (0%)

rewrite381.0ms (1%)

series748.0ms (2%)

simplify85.0ms (0.2%)

prune330.0ms (0.9%)

localize13.0ms (0%)

rewrite262.0ms (0.7%)

series762.0ms (2.1%)

simplify86.0ms (0.2%)

prune192.0ms (0.5%)

regimes26.3s (71.1%)

bsearch212.0ms (0.6%)

simplify5.0ms (0%)

end14.0ms (0%)

sample3.3s (9%)

Profiling