Details

sample22.0ms

Algorithm

intervals

Results

9.0ms

277×

body

valid

simplify80.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	17	5
1	35	5
2	63	4
3	107	4
4	169	4
5	239	4
6	288	4
7	356	4
8	407	4
9	533	4
10	755	4
11	1256	4
12	1302	4
13	1304	4
14	1304	4

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.5b	(fma (/ (- y z) (- a z)) t x)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

10.0ms	(/ (- y z) (- a z))
1.0ms	(fma (/ (- y z) (- a z)) t x)

series135.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ (- y z) (- a z))
80.0ms	(fma (/ (- y z) (- a z)) t x)

simplify68.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	258	433
1	705	410
2	2399	410
3	5001	410

prune212.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

2.5b	(fma (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (cbrt (/ (- y z) (- a z)))) t x)
4.4b	(cbrt (/ (- y z) (- a z)))
4.4b	(cbrt (/ (- y z) (- a z)))
4.4b	(cbrt (/ (- y z) (- a z)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt` `*-un-lft-identity`
93×	`cbrt-prod`
75×	`times-frac`
37×	`add-cube-cbrt`
30×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3--` `pow1/3` `flip--` `div-inv`
1×	`fma-udef`

Counts

4 → 136

Calls

4 calls:

1.0ms	(fma (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (cbrt (/ (- y z) (- a z)))) t x)
8.0ms	(cbrt (/ (- y z) (- a z)))
8.0ms	(cbrt (/ (- y z) (- a z)))
8.0ms	(cbrt (/ (- y z) (- a z)))

series1.1s

Counts

4 → 12

Calls

4 calls:

90.0ms	(fma (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (cbrt (/ (- y z) (- a z)))) t x)
343.0ms	(cbrt (/ (- y z) (- a z)))
354.0ms	(cbrt (/ (- y z) (- a z)))
342.0ms	(cbrt (/ (- y z) (- a z)))

simplify87.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	331	1574
1	733	1516
2	2496	1503
3	5001	1473

prune609.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

1.8b	(cbrt (/ (cbrt (- y z)) (- a z)))
2.5b	(fma (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (* (cbrt (/ (* (cbrt (- y z)) (cbrt (- y z))) 1)) (cbrt (/ (cbrt (- y z)) (- a z))))) t x)
4.4b	(cbrt (/ (- y z) (- a z)))
4.4b	(cbrt (/ (- y z) (- a z)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

133×	`cbrt-prod`
111×	`add-sqr-sqrt` `*-un-lft-identity`
90×	`times-frac`
45×	`add-cube-cbrt`
33×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3--` `pow1/3` `flip--` `div-inv`
1×	`fma-udef`

Counts

4 → 151

Calls

4 calls:

10.0ms	(cbrt (/ (cbrt (- y z)) (- a z)))
1.0ms	(fma (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (* (cbrt (/ (* (cbrt (- y z)) (cbrt (- y z))) 1)) (cbrt (/ (cbrt (- y z)) (- a z))))) t x)
9.0ms	(cbrt (/ (- y z) (- a z)))
8.0ms	(cbrt (/ (- y z) (- a z)))

series1.3s

Counts

4 → 12

Calls

4 calls:

483.0ms	(cbrt (/ (cbrt (- y z)) (- a z)))
100.0ms	(fma (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (* (cbrt (/ (* (cbrt (- y z)) (cbrt (- y z))) 1)) (cbrt (/ (cbrt (- y z)) (- a z))))) t x)
381.0ms	(cbrt (/ (- y z) (- a z)))
373.0ms	(cbrt (/ (- y z) (- a z)))

simplify73.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	553	1961
1	1309	1881
2	5001	1860

prune869.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (/ (- y z) (- a z)) t x))
2.5b	(fma (/ (- y z) (- a z)) t x)
2.5b	(fma (/ (- y z) (- a z)) t x)
2.5b	(fma (/ (- y z) (- a z)) t x)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt (fma (/ (- y z) (- a z)) t x))
1.0ms	(fma (/ (- y z) (- a z)) t x)
1.0ms	(fma (/ (- y z) (- a z)) t x)
1.0ms	(fma (/ (- y z) (- a z)) t x)

series844.0ms

Counts

4 → 12

Calls

4 calls:

576.0ms	(cbrt (fma (/ (- y z) (- a z)) t x))
81.0ms	(fma (/ (- y z) (- a z)) t x)
89.0ms	(fma (/ (- y z) (- a z)) t x)
98.0ms	(fma (/ (- y z) (- a z)) t x)

simplify43.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	118	347
1	274	309
2	1031	306
3	5001	303

prune242.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes327.0ms

Accuracy

80.6% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 1.2b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	17
1	23	17

end0.0ms

sample575.0ms

Algorithm

intervals

Results

287.0ms	8716×	body	80	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid