Details

sample37.0ms

Algorithm

intervals

Results

19.0ms

716×

body

valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	4
1	41	4
2	102	4
3	228	4
4	411	4
5	786	4
6	2469	4
7	5002	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 11.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(cosh x)
0.0b	(* (cosh x) (/ y x))
10.5b	(/ (* (cosh x) (/ y x)) z)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`add-exp-log` `add-cbrt-cube`
13×	`add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-r*`
5×	`pow1` `cbrt-undiv` `cosh-def` `div-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `associate-l` `associate-/r*` `log1p-expm1-u` `associate-/l/` `add-log-exp`
2×	`frac-times` `associate-r/` `associate-l/` `div-inv` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l`

Counts

3 → 74

Calls

3 calls:

1.0ms	(cosh x)
7.0ms	(* (cosh x) (/ y x))
6.0ms	(/ (* (cosh x) (/ y x)) z)

series240.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(cosh x)
82.0ms	(* (cosh x) (/ y x))
114.0ms	(/ (* (cosh x) (/ y x)) z)

simplify54.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	383	433
1	1634	372
2	5001	368

prune168.0ms

Filtered

83 candidates to 65 candidates (78.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	76	7	83
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	8	84

Merged error: 0.0b

Counts

84 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x)
0.0b	(fma (exp x) 1/2 (/ 1/2 (exp x)))
0.0b	(/ 1/2 (exp x))
6.5b	(* (/ y z) (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-cbrt-cube`
19×	`add-exp-log`
13×	`associate-r` `associate-l`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef`

Counts

4 → 120

Calls

4 calls:

3.0ms	(/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x)
1.0ms	(fma (exp x) 1/2 (/ 1/2 (exp x)))
4.0ms	(/ 1/2 (exp x))
10.0ms	(* (/ y z) (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x))

series243.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x)
39.0ms	(fma (exp x) 1/2 (/ 1/2 (exp x)))
8.0ms	(/ 1/2 (exp x))
131.0ms	(* (/ y z) (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x))

simplify63.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	509	1056
1	2478	943
2	5002	942

prune290.0ms

Filtered

132 candidates to 102 candidates (77.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	128	4	132
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	130	10	140

Merged error: 0b

Counts

140 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (exp x) 1/2 (/ 1/2 (exp x)))
0.0b	(* (/ y z) (fma (exp x) 1/2 (/ 1/2 (exp x))))
0.0b	(/ 1/2 (exp x))
6.5b	(/ (* (/ y z) (fma (exp x) 1/2 (/ 1/2 (exp x)))) x)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
20×	`add-cbrt-cube`
19×	`add-exp-log`
13×	`associate-l`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/r*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-r` `fma-udef` `div-inv`
2×	`frac-2neg` `associate-*l/` `clear-num` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `associate-/l/`

Counts

4 → 101

Calls

4 calls:

1.0ms	(fma (exp x) 1/2 (/ 1/2 (exp x)))
6.0ms	(* (/ y z) (fma (exp x) 1/2 (/ 1/2 (exp x))))
4.0ms	(/ 1/2 (exp x))
6.0ms	(/ (* (/ y z) (fma (exp x) 1/2 (/ 1/2 (exp x)))) x)

series281.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(fma (exp x) 1/2 (/ 1/2 (exp x)))
103.0ms	(* (/ y z) (fma (exp x) 1/2 (/ 1/2 (exp x))))
13.0ms	(/ 1/2 (exp x))
130.0ms	(/ (* (/ y z) (fma (exp x) 1/2 (/ 1/2 (exp x)))) x)

simplify61.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	438	829
1	2409	711
2	5001	710

prune233.0ms

Filtered

113 candidates to 84 candidates (74.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	113	10	123

Merged error: 0b

Counts

123 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (exp x) 1/2 (/ 1/2 (exp x)))
0.0b	(/ 1/2 (exp x))
0.2b	(* y (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) z))
6.5b	(/ (* y (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) z)) x)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
20×	`add-cbrt-cube`
19×	`add-exp-log`
13×	`associate-r`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/r*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-l` `div-inv`
2×	`frac-2neg` `associate-*r/` `clear-num` `unswap-sqr`
1×	`pow-prod-down` `*-commutative` `fma-udef` `associate-/l/`

Counts

4 → 99

Calls

4 calls:

1.0ms	(fma (exp x) 1/2 (/ 1/2 (exp x)))
4.0ms	(/ 1/2 (exp x))
6.0ms	(* y (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) z))
6.0ms	(/ (* y (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) z)) x)

series248.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(fma (exp x) 1/2 (/ 1/2 (exp x)))
14.0ms	(/ 1/2 (exp x))
86.0ms	(* y (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) z))
113.0ms	(/ (* y (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) z)) x)

simplify65.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	435	819
1	2282	701
2	5001	701

prune228.0ms

Filtered

111 candidates to 83 candidates (74.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	2	4	6
Picked	1	0	1
Done	0	3	3
Total	113	8	121

Merged error: 0b

Counts

121 → 8

regimes254.0ms

Accuracy

95.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 7.1b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	25
1	34	25

end0.0ms

sample1.0s

Algorithm

intervals

Results

591.0ms

22213×

body

valid