Details

sample27.0ms

Algorithm

intervals

Results

9.0ms	251×	body	80	valid
2.0ms	12×	body	1280	valid
2.0ms	14×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	10×	body	160	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	23	6
1	46	5
2	128	5
3	362	5
4	1024	5
5	2296	5
6	5001	5

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.7b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
14.7b	(fma (- y z) (/ (- t x) (- a z)) x)

rewrite16.0ms

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:

13.0ms	(/ (- t x) (- a z))
0.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

series140.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (- t x) (- a z))
92.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify55.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	268	450
1	733	425
2	2490	423
3	5001	421

prune205.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.9b	(+ (* (- y z) (/ (- t x) (- a z))) x)
7.1b	(* (- y z) (/ (- t x) (- a z)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 126

Calls

3 calls:

13.0ms	(/ (- t x) (- a z))
12.0ms	(+ (* (- y z) (/ (- t x) (- a z))) x)
38.0ms	(* (- y z) (/ (- t x) (- a z)))

series329.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (- t x) (- a z))
149.0ms	(+ (* (- y z) (/ (- t x) (- a z))) x)
127.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	489	904
1	2048	854
2	5001	852

prune344.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
1.2b	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
8.5b	(+ (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))) x)

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`*-un-lft-identity` `add-cbrt-cube`
13×	`associate-r`
10×	`cbrt-prod` `flip3--` `flip--`
9×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `associate-/r/`
6×	`pow1` `frac-times` `add-log-exp`
5×	`associate-l`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-*l/` `log1p-expm1-u`
3×	`associate-*r/` `distribute-lft-out--` `difference-of-squares`
2×	`times-frac` `pow1/3` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

4 → 94

Calls

4 calls:

2.0ms	(cbrt (- t x))
2.0ms	(cbrt (- t x))
60.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
180.0ms	(+ (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))) x)

series730.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (- t x))
152.0ms	(cbrt (- t x))
279.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
152.0ms	(+ (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))) x)

simplify72.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	704	1461
1	2717	1229
2	5001	1155

prune429.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
1.2b	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
11.4b	(fma (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z))) x)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`*-un-lft-identity` `add-cbrt-cube`
13×	`associate-r`
10×	`cbrt-prod` `flip3--` `flip--`
9×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `associate-/r/`
6×	`pow1` `frac-times`
5×	`associate-l`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`associate-*r/` `distribute-lft-out--` `difference-of-squares`
2×	`times-frac` `pow1/3` `unswap-sqr`
1×	`pow-prod-down` `*-commutative` `fma-udef` `div-inv`

Counts

4 → 90

Calls

4 calls:

2.0ms	(cbrt (- t x))
2.0ms	(cbrt (- t x))
64.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
1.0ms	(fma (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z))) x)

series885.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (- t x))
145.0ms	(cbrt (- t x))
282.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
307.0ms	(fma (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z))) x)

simplify64.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	637	1297
1	2410	1119
2	5002	1070

prune391.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 1.9b

regimes397.0ms

Accuracy

-0% (8.7b remaining)

Error of 12.2b against oracle of 3.5b and baseline of 12.2b

bsearch202.0ms

Steps

Iters	Range		Point
7	1.5854851985651301e-09	2.848860754869618e-08	2.319038696069457e-09
9	2.5319273270820795e-306	9.807489329564859e-301	3.092176552363085e-306
6	-7.801819734351108e-196	-1.215551944192786e-196	-1.462651630713459e-196
8	-7.189517843117326e-85	-8.522686855083726e-88	-1.4801961206040853e-87

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 2 (1.0ms)

Iter	Nodes	Cost
0	40	86
1	43	86
2	49	30
3	52	30
4	58	30
5	69	30
6	76	30
7	77	30
8	77	30

end0.0ms

sample730.0ms

Algorithm

intervals

Results

278.0ms	7759×	body	80	valid
66.0ms	492×	body	640	valid
45.0ms	262×	body	1280	valid
41.0ms	414×	body	320	valid
17.0ms	258×	body	160	valid
5.0ms	24×	body	2560	valid