Details

sample25.0ms

Algorithm

intervals

Results

13.0ms

263×

body

valid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	25	8
1	39	8
2	64	8
3	115	8
4	207	8
5	465	8
6	1337	8
7	5001	8

prune3.0ms

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: 7.9b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* t z) x)
0.0b	(- (* y z) x)
0.2b	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
9.9b	(/ (- (* y z) x) (- (* t z) x))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
25×	`times-frac`
24×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`distribute-lft-out`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-/r` `associate-/l`
6×	`prod-diff`
4×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/`
3×	`div-sub`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-exp` `clear-num` `flip-+` `div-inv`
1×	`associate-+r-`

Counts

4 → 113

Calls

4 calls:

4.0ms	(- (* t z) x)
5.0ms	(- (* y z) x)
20.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
10.0ms	(/ (- (* y z) x) (- (* t z) x))

series236.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(- (* t z) x)
23.0ms	(- (* y z) x)
127.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
60.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify73.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	462	1042
1	2015	941
2	5001	941

prune297.0ms

Filtered

125 candidates to 90 candidates (72.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	119	6	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	6	126

Merged error: 0.3b

Counts

126 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (/ y (- (* t z) x)) z x) (* (+ x 1.0) 1))
2.5b	(fma (/ y (- (* t z) x)) z x)
2.6b	(/ x (- (* t z) x))
2.8b	(/ y (- (* t z) x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
15×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`associate-/l*`
7×	`associate-/r*`
6×	`associate-/r/`
5×	`div-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `div-inv`
2×	`flip3--` `associate-*l/` `prod-exp` `flip--`
1×	`flip3-+` `1-exp` `cbrt-unprod` `flip-+` `fma-udef`

Counts

4 → 98

Calls

4 calls:

7.0ms	(/ (fma (/ y (- (* t z) x)) z x) (* (+ x 1.0) 1))
1.0ms	(fma (/ y (- (* t z) x)) z x)
6.0ms	(/ x (- (* t z) x))
6.0ms	(/ y (- (* t z) x))

series279.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (fma (/ y (- (* t z) x)) z x) (* (+ x 1.0) 1))
69.0ms	(fma (/ y (- (* t z) x)) z x)
64.0ms	(/ x (- (* t z) x))
39.0ms	(/ y (- (* t z) x))

simplify61.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	423	735
1	1590	652
2	5001	650

prune351.0ms

Filtered

110 candidates to 88 candidates (80.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	109	7	116

Merged error: 0.2b

Counts

116 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (* y (/ 1 (- (* t z) x))) z x) (* (+ x 1.0) 1))
2.5b	(fma (* y (/ 1 (- (* t z) x))) z x)
2.6b	(/ x (- (* t z) x))
2.8b	(* y (/ 1 (- (* t z) x)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `times-frac`
22×	`add-exp-log` `add-cube-cbrt`
16×	`add-cbrt-cube`
15×	`associate-r`
6×	`pow1` `div-exp` `prod-exp` `associate-/r/` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `cbrt-unprod` `div-inv` `unswap-sqr`
2×	`flip3--` `frac-2neg` `1-exp` `associate-*l/` `clear-num` `flip--`
1×	`rec-exp` `flip3-+` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `flip-+` `fma-udef`

Counts

4 → 107

Calls

4 calls:

7.0ms	(/ (fma (* y (/ 1 (- (* t z) x))) z x) (* (+ x 1.0) 1))
1.0ms	(fma (* y (/ 1 (- (* t z) x))) z x)
7.0ms	(/ x (- (* t z) x))
12.0ms	(* y (/ 1 (- (* t z) x)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (fma (* y (/ 1 (- (* t z) x))) z x) (* (+ x 1.0) 1))
70.0ms	(fma (* y (/ 1 (- (* t z) x))) z x)
74.0ms	(/ x (- (* t z) x))
37.0ms	(* y (/ 1 (- (* t z) x)))

simplify73.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	510	828
1	2145	713
2	5001	701

prune352.0ms

Filtered

119 candidates to 91 candidates (76.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	119	7	126

Merged error: 0.2b

Counts

126 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* y z) x)
0.2b	(/ (+ x (/ 1 (/ (- (* t z) x) (- (* y z) x)))) (+ x 1.0))
0.3b	(/ 1 (/ (- (* t z) x) (- (* y z) x)))
9.8b	(/ (- (* t z) x) (- (* y z) x))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

110×	`times-frac`
95×	`*-un-lft-identity`
68×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`associate-/r*`
19×	`add-exp-log`
16×	`distribute-lft-out`
13×	`associate-/r/` `add-cbrt-cube`
12×	`div-inv`
11×	`associate-/l*`
9×	`div-exp`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`frac-2neg` `prod-diff` `clear-num`
2×	`rec-exp` `flip3-+` `1-exp` `flip-+`
1×	`sub-neg` `pow-flip` `fma-neg` `diff-log` `div-sub` `inv-pow`

Counts

4 → 185

Calls

4 calls:

5.0ms	(- (* y z) x)
25.0ms	(/ (+ x (/ 1 (/ (- (* t z) x) (- (* y z) x)))) (+ x 1.0))
12.0ms	(/ 1 (/ (- (* t z) x) (- (* y z) x)))
11.0ms	(/ (- (* t z) x) (- (* y z) x))

series379.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(- (* y z) x)
183.0ms	(/ (+ x (/ 1 (/ (- (* t z) x) (- (* y z) x)))) (+ x 1.0))
99.0ms	(/ 1 (/ (- (* t z) x) (- (* y z) x)))
70.0ms	(/ (- (* t z) x) (- (* y z) x))

simplify121.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	676	2096
1	3331	1893
2	5001	1810

prune393.0ms

Filtered

197 candidates to 117 candidates (59.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	197	7	204

Merged error: 0.2b

Counts

204 → 7

regimes185.0ms

Accuracy

41.5% (2.5b remaining)

Error of 2.8b against oracle of 0.3b and baseline of 4.6b

bsearch134.0ms

Steps

Iters	Range		Point
9	1.8652500212734269e-07	0.019205428735188275	7.361573319340001e-05
8	-6.821300429682039e+69	-1.1151701921709721e+67	-1.1274418778118125e+67

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	23
1	42	23
2	42	23

end0.0ms

sample632.0ms

Algorithm

intervals

Results

403.0ms

8312×

body

valid

Details

sample25.0ms

simplify63.0ms

prune3.0ms

localize12.0ms

rewrite43.0ms

series236.0ms

simplify73.0ms

prune297.0ms

localize14.0ms

rewrite23.0ms

series279.0ms

simplify61.0ms

prune351.0ms

localize17.0ms

rewrite30.0ms

series287.0ms

simplify73.0ms

prune352.0ms

localize14.0ms

rewrite60.0ms

series379.0ms

simplify121.0ms

prune393.0ms

regimes185.0ms

bsearch134.0ms

simplify3.0ms

end0.0ms

sample632.0ms

Profiling